Crc interleaving pattern for polar codes

ABSTRACT

According to some embodiments, a method of operation of a wireless transmitter in a wireless communication network comprises: encoding a set of information carrying data bits u of length K with a linear outer code to generate a set of outer parity bits p along with the data bits u; interleaving the set of outer parity bits p and the data bits u using a predetermined interleaving mapping function that depends on the number of data bits K and is operable to distribute some bits of the set of parity bits p in front of some data bits u; and encoding the interleaved bits using a Polar encoder to generate a set of encoded bits x. Various interleaving mapping functions are disclosed.

TECHNICAL FIELD

Particular embodiments are directed to wireless communications and, moreparticularly, to cyclic redundancy check (CRC) interleaving patterns forpolar codes.

INTRODUCTION

Polar codes, proposed by E. Arikan, “Channel Polarization: A Method forConstructing Capacity-Achieving Codes for Symmetric Binary-InputMemoryless Channels,” IEEE Transactions on Information Theory, vol. 55,pp. 3051-3073, July 2009, are a class of constructive coding schemesthat achieve the symmetric capacity of the binary-input discretememoryless channels under a low-complexity Successive Cancellation (SC)decoder. The finite-length performance of polar codes under SC, however,is not competitive compared to other modern channel coding schemes suchas low-density parity-check (LDPC) codes and Turbo codes. An SC list(SCL) decoder is proposed in I. Tal and A. Vardy, “List Decoding ofPolar Codes,” Proceedings of IEEE Symp. Inf. Theory, pp. 1-5, 2011, thatapproaches the performance of optimal maximum-likelihood (ML) decoder.By concatenating a simple cyclic redundancy check (CRC) coding, theperformance of a concatenated polar code is competitive with that ofwell-optimized LDPC and Turbo codes. As a result, polar codes are beingconsidered as a candidate for future fifth generation (5G) wirelesscommunication systems.

Polar coding transforms a pair of identical binary-input channels intotwo distinct channels of different qualities, one better and one worsethan the original binary-input channel Repeating such a pair-wisepolarizing operation on a set of N=2^(n) independent uses of abinary-input channel results in a set of 2^(n) “bit-channels” of varyingqualities. Some of the bit channels are nearly perfect (i.e., errorfree) while the rest of them are nearly useless (i.e., totally noisy).Polar coding uses the nearly perfect channel to transmit data to thereceiver and sets the input to the useless channels to have fixed orfrozen values (e.g., 0) known to the receiver. For this reason, theinput bits to the nearly useless and the nearly perfect channel arecommonly referred to as frozen bits and non frozen (or information)bits, respectively. Only the non-frozen bits are used to carry data in apolar code. Loading the data into the proper information bit locationshas direct impact on the performance of a polar code. The set ofinformation bit locations is commonly referred to as an information set.An illustration of the structure of a length-8 polar code is illustratedin FIG. 1.

Although the original polar code, as proposed by Arikan, was proven tobe capacity achieving with a low-complexity successive cancellation (SC)decoder, the finite-length performance of polar codes under SC is notcompetitive compared to other modern channel coding schemes such LDPCand Turbo codes. A more complex decoder, the SC list (SCL) decoder, isproposed in I. Tal and A. Vardy, “List Decoding of polar codes,” inProceedings of IEEE Symp. Inf. Theory, pp. 1-5, 2011, where a list ofmore than one surviving decision paths is maintained in the decodingprocess, but the resulting performance is still unsatisfactory. Tal etal. further proposed that by concatenating a linear outer code, a cyclicredundancy check (CRC) code, with the original polar code as inner code,the outer code can be used to check if any of the candidate paths in thelist is correctly decoded. Such a two-step decoding processsignificantly improves the performance and makes polar codes competitivewith that of well-optimized LDPC and Turbo codes. However, the two-stepdecoding process is in general sub-optimal because each step does notaccount for the structure of the other (inner or outer) code.

The two-step decoding process also increases the decoding latency as theouter decoder typically needs to wait for the inner decoder to finishdecoding before it operates. To compensate for the delay incurred byextra processing, methods of improving the average decoding latency areneeded. One method is to try to terminate the decoding when one ofdecoded CRC bits is found to be inconsistent with the previously decodedinformation bits that the CRC bit depends upon. However, this method isnot effective when all CRC bits are attached at the end of the codeblock.

SUMMARY

The embodiments described herein include applying a bit-interleaver witha specific interleaving pattern between a linear outer code (e.g., acyclic redundancy check (CRC) code) and a polar inner code. Theinterleaving pattern enables the decoder to achieve early termination ofthe decoding when some of the CRC bits that are encountered early in thesuccessive decoding process are used for early error detection, whilemaintaining a low false-alarm rate (FAR). In addition, the interleaveralso enables some of the parity bits generated by the outer code to beused earlier to positively influence the decisions made in a modifiedsuccessive cancellation list (SCL) decoder for the polar inner code.This facilitates a single-step decoding for the overall concatenatedcode that accounts for the structure of the outer code and thusoutperforms its two-step counterpart.

According to some embodiments, a method of operation of a wirelesstransmitter in a wireless communication network comprises: encoding aset of information carrying data bits u of length K with a linear outercode to generate a set of outer parity bits p along with the data bitsu; interleaving the set of outer parity bits p and the data bits u usinga predetermined interleaving mapping function that depends on the numberof data bits K and is operable to distribute some bits of the set ofparity bits p in front of some data bits u; and encoding the interleavedbits using a polar encoder to generate a set of encoded bits x. Themethod may further comprise transmitting the set of encoded bits x to awireless receiver.

In particular embodiments the predetermined interleaving mappingfunction comprises a template interleaver for a largest value of K,referred to a K_(max), and the template interleaver comprises ahigh-index bit mapper wherein the K data bits are loaded at thehigh-index positions of the input of the template interleaver, whereu=[u₀, u₁, . . . , u_(K-1)] and the input of the template interleaver,denoted by v=[v₀, v₁, . . . , v_(K) _(max) ₋₁], is given by thefollowing bit mapping:

$v_{i} = \left\{ {\begin{matrix}u_{i - K_{\max} + K} & {{K_{\max} - K} \leq i < K_{\max}} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {otherwise}\end{matrix}.} \right.$

In some embodiments the template interleaver comprises a low-index bitmapper wherein: the K data bits are loaded at the low-index positions ofthe input of the template interleaver in reverse, where the input of thetemplate interleaver is given by the following bit mapping:

${v_{i} = \left\{ \begin{matrix}u_{K - 1 - i} & {0 \leq i < K} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {{othe}r{wise}}\end{matrix} \right.}.$

According to some embodiments, a wireless transmitter comprisesprocessing circuitry. The processing circuitry is operable to: encode aset of information carrying data bits u of length K with a linear outercode to generate a set of outer parity bits p along with the data bitsu; interleave the set of outer parity bits p and the data bits u using apredetermined interleaving mapping function that depends on the numberof data bits K and is operable to distribute some bits of the set ofparity bits p in front of some data bits u; and encode the interleavedbits using a polar encoder to generate a set of encoded bits x. Theprocessing circuitry may be further operable to transmit the set ofencoded bits x to a wireless receiver.

In particular embodiments, the wireless transmitter comprises aswireless device (e.g., user equipment) or a base station (e.g., gNB).

According to some embodiments, a method of operation of a wirelessreceiver in a wireless communication network comprises: determining adecoder reaches a distributed CRC bit p_(i) when decoding a received setof polar encoded bits; calculating L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(

), determining whether the info bits associated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminating the decoding; and upon determining there exists asuccessful parity check, continuing the decoding.

According to some embodiments, a method of operation of a wirelessreceiver in a wireless communication network comprises: determining adecoder reaches a distributed CRC bit p_(i) when decoding a received setof polar encoded bits, wherein the distributed CRC bit p_(i) is maskedby a bit q_(i), and becomes: w_(i)=(p_(i)+q_(i)) mod 2; calculating Lestimated values, w_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each w_(i)(

), removing the mask, p_(i)=(w_(i)+q_(i)) mod 2; for each p_(i)(

), determining whether the info bits associated with p_(i)(

) leads to a successful parity check; upon determining there is nosuccessful parity check for each p_(i)(

), terminating the decoding; and upon determining there exists asuccessful parity check, continuing the decoding.

In particular embodiments, the decoding comprises a templatedeinterleaver and a bit demapper which performs the inverse of the bitmapping of any of the interleaving functions described herein.

According to some embodiments, a wireless receiver comprises processingcircuitry. The processing circuitry is operable to: determine a decoderreaches a distributed CRC bit p_(i) when decoding a received set ofpolar encoded bits; calculate L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(

), determine whether the info bits associated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminate the decoding; and upon determining there exists asuccessful parity check, continue the decoding.

According to some embodiments, a wireless receiver comprises processingcircuitry. The processing circuitry is operable to: determine a decoderreaches a distributed CRC bit p_(i) when decoding a received set ofpolar encoded bits, wherein the distributed CRC bit p is masked by a bitq_(i), and becomes: w_(i)=(p_(i)+q_(i)) mod 2; calculate L estimatedvalues, w_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each w_(i)(

), remove the mask, p_(i)=(w_(i)+q_(i)) mod 2; for each p_(i)(

), determine whether the info bits associated with p_(i)(

) leads to a successful parity check; upon determining there is nosuccessful parity check for each p_(i)(e), terminate the decoding; andupon determining there exists a successful parity check, continue thedecoding.

According to some embodiments, a wireless transmitter comprises anencoding module (1350, 1450). The encoding module is operable to: encodea set of information carrying data bits u of length K with a linearouter code to generate a set of outer parity bits p along with the databits u; interleave the set of outer parity bits p and the data bits uusing a predetermined interleaving mapping function that depends on thenumber of data bits K and is operable to distribute some bits of the setof parity bits p in front of some data bits u; and encode theinterleaved bits using a polar encoder to generate a set of encoded bitsx.

According to some embodiments, a wireless receiver comprises a decodingmodule (1350, 1450). The decoding module is operable to: determine adecoder reaches a distributed CRC bit p_(i) when decoding a received setof polar encoded bits; calculate L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(e), determine whether the info bitsassociated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminate the decoding; and upon determining there exists asuccessful parity check, continue the decoding.

According to some embodiments, a wireless receiver comprises a decodingmodule (1350, 1450). The decoding module is operable to: determine adecoder reaches a distributed CRC bit p_(i) when decoding a received setof polar encoded bits, wherein the distributed CRC bit p_(i) is maskedby a bit q_(i), and becomes: w_(i)=(p_(i)+q_(i)) mod 2; calculate Lestimated values, w_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each w_(i)(

), remove the mask, p_(i)=(w_(i)+q_(i)) mod 2; for each p_(i)(

), determine whether the info bits associated with p_(i)(

) leads to a successful parity check; upon determining there is nosuccessful parity check for each p_(i)(e), terminate the decoding; andupon determining there exists a successful parity check, continue thedecoding.

In particular embodiments, the wireless receiver comprises as wirelessdevice (e.g., user equipment) or a base station (e.g., gNB).

Also disclosed is a computer program product. The computer programproduct comprises instructions stored on non-transient computer-readablemedia which, when executed by a processor, perform the steps of encodinga set of information carrying data bits u of length K with a linearouter code to generate a set of outer parity bits p along with the databits u; interleaving the set of outer parity bits p and the data bits uusing a predetermined interleaving mapping function that depends on thenumber of data bits K and is operable to distribute some bits of the setof parity bits p in front of some data bits u; and encoding theinterleaved bits using a Polar encoder to generate a set of encoded bitsx. The instructions may further perform the step of transmitting the setof encoded bits x to a wireless receiver.

Another computer program product comprises instructions stored onnon-transient computer-readable media which, when executed by aprocessor, perform the steps of determining a decoder reaches adistributed CRC bit p_(i) when decoding a received set of polar encodedbits; calculating L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(

), determining whether the info bits associated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminating the decoding; and upon determining there exists asuccessful parity check, continuing the decoding Another computerprogram product comprises instructions stored on non-transientcomputer-readable media which, when executed by a processor, perform thesteps o determining a decoder reaches a distributed CRC bit p_(i) whendecoding a received set of polar encoded bits, wherein the distributedCRC bit p_(i) is masked by a bit q_(i), and becomes: w_(i)=(p_(i)+q_(i))mod 2; calculating L estimated values, w_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each w_(i)(

), removing the mask, p_(i)=(w_(i)+q_(i)) mod 2; for each p_(i)(

), determining whether the info bits associated with p_(i)(

) leads to a successful parity check; upon determining there is nosuccessful parity check for each p_(i)(

), terminating the decoding; and upon determining there exists asuccessful parity check, continuing the decoding.

Particular embodiments may include some, all, or none of the followingadvantages. For example, particular interleaving patterns enable thedecoder to take early termination of decoding if the decoded info bitsin each candidate of the decoding list are not consistent with thedecoded value of a CRC bit. This reduces the overall decoding latency.With existing methods, the entire length-K_(CRC) vector of CRC bits aretypically used in CRC checking after all information bits are decoded.With particular embodiments described herein, CRC checking can be donebit-by-bit for each individual CRC bit during the successivecancellation list decoding. The interleaving patterns strike a balancebetween early termination gain in decoding and the false-alarmprobability (i.e., the probability of falsely accepting an incorrectlydecoded code block).

Particular embodiments also facilitate a single-step decoding processfor the concatenation of any linear outer code and a polar inner codethrough a judicious design of the interleaver, as opposed to a two-stepdecoding process where the inner polar code is first decoded followed bythe decoding of the outer code. Such a single step decoding jointlyaccounts the structure of the polar inner code and the linear outer(e.g., CRC) code and thus improves the performance, compared to thetwo-step solution.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the embodiments and their featuresand advantages, reference is now made to the following description,taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates an example of a polar code structure with N=8;

FIG. 2 is a block diagram illustrating an example wireless network,according to a particular embodiment;

FIG. 3 is a block diagram illustrating the encoder structure of aninterleaved concatenated Polar code, according to a particularembodiment;

FIG. 4 is a block diagram illustrating a one-step decoder structure ofan interleaved concatenated Polar code, according to a particularembodiment;

FIG. 5 is a block diagram illustrating a template interleave of a fixedsize K_(max), according to a particular embodiment;

FIG. 6 is a block diagram illustrating the structure of a deinterleaver,according to a particular embodiment;

FIG. 7 is a flow diagram illustrating an example method in a wirelesstransmitter, according to particular embodiments;

FIG. 8 is a flow diagram illustrating an example method in a wirelessreceiver, according to particular embodiments;

FIG. 9A is a block diagram illustrating an example embodiment of awireless device;

FIG. 9B is a block diagram illustrating example components of a wirelessdevice;

FIG. 10A is a block diagram illustrating an example embodiment of anetwork node; and

FIG. 10B is a block diagram illustrating example components of a networknode.

DETAILED DESCRIPTION

Polar codes achieve the symmetric capacity of the binary-input discretememoryless channels under a low-complexity successive cancellation (SC)decoder. However, the finite-length performance of polar codes under SCis not competitive compared to other modern channel coding schemes suchas low-density parity-check (LDPC) codes and Turbo codes. An SC list(SCL) decoder approaches the performance of optimal maximum-likelihood(ML) decoder. By concatenating a simple cyclic redundancy check (CRC)coding, the performance of a concatenated polar code is competitive withthat of well-optimized LDPC and Turbo codes. As a result, polar codesmay be used for fifth generation (5G) wireless communication systems.

By concatenating a linear outer code, such as a CRC code, with theoriginal polar code as inner code, the outer code can be used to checkif any of the candidate paths in the list is correctly decoded. Thetwo-step decoding process significantly improves the performance,however, it is in general sub-optimal because each step does not accountfor the structure of the other (inner or outer) code.

The two-step decoding process also increases the decoding latency as theouter decoder typically needs to wait for the inner decoder to finishdecoding before it operates. To compensate for the delay incurred byextra processing, particular embodiments improve the average decodinglatency.

Particular embodiments described herein obviate the problems describedabove and include applying a bit-interleaver with a specificinterleaving pattern between a linear outer code (e.g., a CRC code) anda polar inner code. The interleaving pattern enables the decoder toachieve early termination of the decoding when some of the CRC bits thatare encountered early in the successive decoding process are used forearly error detection, while maintaining a low false-alarm rate (FAR).In addition, the interleaver also enables some of the parity bitsgenerated by the outer code to be used earlier to positively influencethe decisions made in a modified SCL decoder for the polar inner code.This facilitates a single-step decoding for the overall concatenatedcode that accounts for the structure of the outer code and thusoutperforms its two-step counterpart.

The interleaving patterns strike a balance between early terminationgain in decoding and the false-alarm probability (i.e., the probabilityof falsely accepting an incorrectly decoded code block). Particularembodiments also facilitate a single-step decoding process for theconcatenation of any linear outer code and a polar inner code through ajudicious design of the interleaver, as opposed to a two-step decodingprocess where the inner polar code is first decoded followed by thedecoding of the outer code. Such a single step decoding jointly accountsfor the structure of the polar inner code and the linear outer (CRC)code and thus improves the performance, compared to the two-stepsolution.

The following description sets forth numerous specific details. It isunderstood, however, that embodiments may be practiced without thesespecific details. In other instances, well-known circuits, structuresand techniques have not been shown in detail in order not to obscure theunderstanding of this description. Those of ordinary skill in the art,with the included descriptions, will be able to implement appropriatefunctionality without undue experimentation.

References in the specification to “one embodiment,” “an embodiment,”“an example embodiment,” etc., indicate that the embodiment describedmay include a particular feature, structure, or characteristic, butevery embodiment may not necessarily include the particular feature,structure, or characteristic. Moreover, such phrases are not necessarilyreferring to the same embodiment. Further, when a particular feature,structure, or characteristic is described in connection with anembodiment, it is submitted that it is within the knowledge of oneskilled in the art to implement such feature, structure, orcharacteristic in connection with other embodiments, whether or notexplicitly described.

Particular embodiments are described with reference to FIGS. 2-10B ofthe drawings, like numerals being used for like and corresponding partsof the various drawings.

Long term evolution (LTE) and NR are used throughout this disclosure asan example cellular system, but the ideas presented herein may apply toother wireless communication systems as well.

FIG. 2 is a block diagram illustrating an example wireless network,according to a particular embodiment. Wireless network 100 includes oneor more wireless devices 110 (such as mobile phones, smart phones,laptop computers, tablet computers, MTC devices, or any other devicesthat can provide wireless communication) and a plurality of networknodes 120 (such as base stations, eNodeBs, gNBs, etc.). Wireless device110 may also be referred to as a UE. Network node 120 serves coveragearea 115 (also referred to as cell 115).

In general, wireless devices 110 that are within coverage of networknode 120 (e.g., within cell 115 served by network node 120) communicatewith network node 120 by transmitting and receiving wireless signals130. For example, wireless devices 110 and network node 120 maycommunicate wireless signals 130 containing voice traffic, data traffic,and/or control signals. A network node 120 communicating voice traffic,data traffic, and/or control signals to wireless device 110 may bereferred to as a serving network node 120 for the wireless device 110.Communication between wireless device 110 and network node 120 may bereferred to as cellular communication. Wireless signals 130 may includeboth downlink transmissions (from network node 120 to wireless devices110) and uplink transmissions (from wireless devices 110 to network node120).

Each network node 120 may have a single transmitter or multipletransmitters for transmitting signals 130 to wireless devices 110. Insome embodiments, network node 120 may comprise a multi-inputmulti-output (MIMO) system. Wireless signal 130 may comprise one or morebeams. Particular beams may be beamformed in a particular direction.Each wireless device 110 may have a single receiver or multiplereceivers for receiving signals 130 from network nodes 120 or otherwireless devices 110. Wireless device 110 may receive one or more beamscomprising wireless signal 130.

Wireless signals 130 may be transmitted on time-frequency resources. Thetime-frequency resources may be partitioned into radio frames,subframes, slots, and/or mini-slots. Network node 120 may dynamicallyschedule subframes/slots/mini-slots as uplink, downlink, or acombination uplink and downlink. Different wireless signals 130 mayinclude different transmission processing times.

Network node 120 may operate in a licensed frequency spectrum, such asan LTE spectrum. Network node 120 may also operate in an unlicensedfrequency spectrum, such as a 5 GHz Wi-Fi spectrum. In an unlicensedfrequency spectrum, network node 120 may coexist with other devices suchas IEEE 802.11 access points and terminals. To share the unlicensedspectrum, network node 120 may perform listen-before-talk (LBT)protocols before transmitting or receiving wireless signals 130.Wireless device 110 may also operate in one or both of licensed orunlicensed spectrum and in some embodiments may also perform LBTprotocols before transmitting wireless signals 130. Both network node120 and wireless device 110 may also operate in licensed sharedspectrum.

For example, network node 120 a may operate in a licensed spectrum andnetwork node 120 b may operate in an unlicensed spectrum. Wirelessdevice 110 may operate in both licensed and unlicensed spectrum. Inparticular embodiments, network nodes 120 a and 120 b may beconfigurable to operate in a licensed spectrum, an unlicensed spectrum,a licensed shared spectrum, or any combination. Although the coveragearea of cell 115 b is illustrated as included in the coverage area ofcell 115 a, in particular embodiments the coverage areas of cells 115 aand 115 b may overlap partially or may not overlap at all.

In particular embodiments, wireless device 110 and network nodes 120 mayperform carrier aggregation. For example, network node 120 a may servewireless device 110 as a PCell and network node 120 b may serve wirelessdevice 110 as a SCell. Network nodes 120 may perform self-scheduling orcross-scheduling. If network node 120 a is operating in licensedspectrum and network node 120 b is operating in unlicensed spectrum,network node 120 a may provide license assisted access to the unlicensedspectrum (i.e., network node 120 a is a LAA PCell and network node 120 bis a LAA SCell).

In particular embodiments, wireless signals 130 may be encoded using apolar code. For example, wireless device 110 and/or network node 120 mayuse a polar code for encoding wireless signal 130. In some embodiments,the encoding may include an interleaver. The interleaver is described inmore detail with respect to FIGS. 3-8.

In wireless network 100, each network node 120 may use any suitableradio access technology, such as long term evolution (LTE),LTE-Advanced, UMTS, HSPA, GSM, cdma2000, NR, WiMax, WiFi, and/or othersuitable radio access technology. Wireless network 100 may include anysuitable combination of one or more radio access technologies. Forpurposes of example, various embodiments may be described within thecontext of certain radio access technologies. However, the scope of thedisclosure is not limited to the examples and other embodiments coulduse different radio access technologies.

As described above, embodiments of a wireless network may include one ormore wireless devices and one or more different types of radio networknodes capable of communicating with the wireless devices. The networkmay also include any additional elements suitable to supportcommunication between wireless devices or between a wireless device andanother communication device (such as a landline telephone). A wirelessdevice may include any suitable combination of hardware and/or software.For example, in particular embodiments, a wireless device, such aswireless device 110, may include the components described with respectto FIG. 9A below. Similarly, a network node may include any suitablecombination of hardware and/or software. For example, in particularembodiments, a network node, such as network node 120, may include thecomponents described with respect to FIG. 10A below.

Particular embodiments include a judiciously designed interleaver, withspecific interleaver patterns, between a linear outer code and a polarinner code. The interleaving patterns move the CRC bits to the beginningof the code blocks so that the decoding process may be terminatedearlier to reduce average latency if the decoded values of some CRC bitsare inconsistent with the values of the corresponding information bits.These interleaving patterns are designed in such a way that the earlytermination gain is maximized while maintain a low FAR.

According to particular embodiments of the interleaver, a single-pass orsingle-step decoding is performed using a slightly modified SCL polardecoder to jointly take advantage of the structure of both the inner andouter coder. The interleaver enables some of the parity bits generatedby the outer code to be used earlier to positively influence thedecisions made in a modified SCL decoder for the polar inner code. Thisfacilitates a single-step decoding for the overall concatenated codewhile outperforming its two-step counterpart.

Particular embodiments include an interleaver with a specificinterleaving pattern, for each possible number of information bits,between a linear outer code, such as a CRC code, and a polar inner code.The interleaver distributes some CRC bits in front of some informationbits. This enables a SCL decoder to terminate the decoding process whenthe decoded value of any of these CRC bits is not consistent with theinformation bits that the CRC bits depend upon for every candidate inthe list Interleaving of CRC bits also facilitates list decoding for theinner polar code that accounts for the dependency structure of theparity bits and the data bits from the outer code. An example isillustrated in FIG. 3.

FIG. 3 is a block diagram illustrating the encoder structure of aninterleaved concatenated polar code, according to a particularembodiment. The information-carrying data bits u of length K are firstencoded by a linear outer encoder 10 (the linear outer code is typicallya CRC code) to generate a number of outer parity bits p along with thedata bits u. All the bits x_(outer)=[u|p] are interleaved at interleaver12 and put into polar inner encoder 14 along with the frozen bits toform the input to polar inner encoder 14, which generates the overallcoded bits x. Interleaver 12 operates based on a predeterminedinterleaving mapping ϕ_(K)(•), which depends on the number of data bits,K.

FIG. 4 is a block diagram illustrating a one-step decoder structure ofan interleaved concatenated polar code, according to a particularembodiment. At the receiver, the input log-likelihood ratios (LLRs) y ofthe coded bits are first decoded using modified SCL polar decoder 16,whose outputs are then passed through deinterleaver 18 that extracts thedecoded data bits. Deinterleaver 18 depends on the interleaving mappingϕ_(K) (•) used in the encoder 14 in a straightforward manner. Theoperations of the modified SCL polar decoder is similar to an ordinarySCL polar decoder except that whenever an outer parity bit is reached,as indicated by the interleaving mapping ϕ_(K)(•), during the successivedecoding process, its value is computed based on the previous data bitsas indicated by the corresponding columns of the generating matrix G_(o)of the outer code.

The size of the interleaver described with respect to FIG. 3, forexample, generally depends on the number K of data bits as well as thenumber n_(CRC) of CRC bits. To ease implementation, particularembodiments implement a single template interleaver ϕ_(T)(•) at thelargest possible value of K, dented by K_(max), and then use a subset ofthis template interleaver to implement the interleaver needed for anygiven value of K in FIG. 3.

FIG. 5 is a block diagram illustrating a template interleaver of a fixedsize K_(max), according to a particular embodiment. Interleaver 30comprises bit mapper 20, template interleaver 22, and bit extractor 24.Bit mapper 20 maps K data bits into certain input positions of templateinterleaver 22 of size K_(max). Bit mapper μ_(K)(•) depends on K. Then_(CRC) CRC bits are mapped into other input positions. The rest of theinput positions are filled with NULL. Template interleaver 22 re-ordersthe data bits, CRC bits, and NULLs. Bit extractor 24 removes the NULLsfrom the output of template interleaver 22 to form the output ofinterleaver 30.

The design of the template interleaver is tied to that of the bitmapper. The following are two examples of a bit mapper. A high-index bitmapper loads the K data bits at the high-index positions of the input ofthe template interleaver. Specifically, let u=[u₀, u₁, . . . , u_(K-1)]be the data bits. Then the input of the template interleaver, denoted byv=[v₀, v₁, . . . , v_(K) _(max) ₋₁], is given by the following bitmapping:

$v_{i} = \left\{ {\begin{matrix}u_{i - K_{\max} + K} & {{K_{\max} - K} \leq i < K_{\max}} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {otherwise}\end{matrix}.} \right.$

FIGS. 5 and 6 describe the interleaving and de-interleaving operationsfor a high-index bit mapper.

Another example includes a low-index bit mapper. The low-index bitmapper loads the K data bits at the low-index positions of the input ofthe template interleaver in a reversed manner. Specifically, the inputof the template interleaver is given by the following bit mapping

${v_{i} = \left\{ \begin{matrix}u_{K - 1 - i} & {0 \leq i < K} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {{othe}r{wise}}\end{matrix} \right.}.$

FIG. 6 is a block diagram illustrating the structure of a deinterleaver,according to a particular embodiment. Deinterleaver 40 includes nullfiller 26, template deinterleaver 28, and bit demapper 32. The exampledeinterleaver illustrates the corresponding inverse operations in thedeinterleaver of the decoder illustrated in FIG. 4.

After polar decoding, the output of the polar decoder is input todeinterleaver 40. Null filler 26 fills the input with NULLs according tothe same NULL positions as used in bit extractor 24 in FIG. 5. Templatedeinterleaver 40 deinterleaves the null-filled sequence.

Part of the output of the template deinterleaver forms the decoded outer(CRC) parity bits and part of the output is passed through bit demapper32, which performs the inverse operation of the bit mapping performed inFIG. 4. The output of bit demapper 32 is the decoded data bits. In thecase of the outer code being a CRC code used for error detection, thedecoded data bits and decoded outer CRC parity bits are usedsubsequently to check if the CRC passes to detect whether an error hasoccurred.

Particular embodiments may include any of a number of judiciouslydesigned interleaving patterns for the template interleaver from whichthe corresponding interleaver for each possible number of informationbits can be derived. Particular patterns maximize the potentialreduction in decoding latency through earlier termination whilemaintaining the FAR.

Listed below are some example interleaving patterns for the templateinterleaver, each associated with a particular bit mapper describedabove. In all cases, the following two CRC polynomials are used asexamples.

g _(crc)(D)=D ²⁴ +D ²³ +D ²¹ +D ²⁰ +D ¹⁷ +D ¹⁵ +D ¹³ +D ¹² +D ⁸ +D ⁴ +D² +D+1

g _(crc)(D)=D ¹⁹ +D ¹⁶ +D ¹⁴ +D ¹³ +D ¹² +D ¹⁰ +D ⁸ +D ⁷ +D ⁴ +D ³+1

Because the template interleaver ϕ_(T)(•) is a mapping from integers tointegers, it can be equivalently described using an integer sequence,denoted by ϕ_(T). The indices corresponding to the CRC bits areunderlined.

As examples, value of K_(max) is assumed to be in the set {53, 72, 140,160, 200}, which are values likely to be used in 5G-NR systems, togenerate the following interleaving patterns.

1. For high-index bit mapper for K_(max)=53

-   -   (a) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46        48 51 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41        50 61 0 34 36 43 53 40 49 54 29 42 64 13 65 2 62 23 55 69 71 3        56 57 67 6 59 60 63 66 70];    -   (b) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46        48 51 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41        50 61 0 2 3 6 13 23 29 34 36 40 42 43 49 53 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (c) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46        48 51 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41        50 61 0 34 36 43 53 2 3 6 13 23 29 40 42 49 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (d) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46        48 51 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41        50 61 0 34 36 43 53 40 49 54 2 3 6 13 23 29 42 55 56 57 59 60 62        63 64 65 66 67 69 70 71];

2. For low-index bit mapper for K_(max)=53

-   -   (a) ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47        48 51 58 5 13 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45        61 9 16 18 52 53 3 12 54 10 23 64 39 65 50 62 29 55 69 71 49 56        57 67 46 59 60 63 66 70];    -   (b) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6        4 1 0 58 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2        61 52 18 16 9 53 12 3 54 23 10 64 39 65 50 62 29 55 69 71 49 56        67 57 46 59 66 60 70 63];    -   (c) ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47        48 51 58 5 13 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45        61 3 9 10 12 16 18 23 29 39 46 49 50 52 53 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (d) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6        4 1 0 58 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2        61 3 9 10 12 16 18 23 29 39 46 49 50 52 53 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (e) ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47        48 51 58 5 13 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45        61 9 16 18 52 53 3 10 12 23 29 39 46 49 50 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (f) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6        4 1 0 58 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2        61 52 18 16 9 53 3 10 12 23 29 39 46 49 50 54 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (g) ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47        48 51 58 5 13 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45        61 9 16 18 52 53 3 12 54 10 23 29 39 46 49 50 55 56 57 59 60 62        63 64 65 66 67 69 70 71];    -   (h) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6        4 1 0 58 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2        61 52 18 16 9 53 12 3 54 10 23 29 39 46 49 50 55 56 57 59 60 62        63 64 65 66 67 69 70 71];

3. For high-index bit mapper for K_(max)=72

-   -   (a) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 41 43 44 45 47        49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 29 33        35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 19 55 59 68        73 32 53 61 84 10 62 72 21 81 48 83 22 76 42 88 2 74 75 25 82 85        6 78 79 86 89 90];    -   (b) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 41 43 44 45 47        49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 29 33        35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 2 6 10 19 21        22 25 32 42 48 53 55 59 61 62 68 72 73 74 75 76 78 79 81 82 83        84 85 86 88 89 90];    -   (c) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 41 43 44 45 47        49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 29 33        35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 19 55 59 68        73 2 6 10 21 22 25 32 42 48 53 61 62 72 74 75 76 78 79 81 82 83        84 85 86 88 89 90];    -   (d) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 41 43 44 45 47        49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 29 33        35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 19 55 59 68        73 32 53 61 84 2 6 10 21 22 25 42 48 62 72 74 75 76 78 79 81 82        83 85 86 88 89 90];

4. For low-index bit mapper for K_(max)=72

-   -   (a) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 47        51 55 59 62 64 66 77 2 11 25 34 35 43 45 56 71 80 3 12 16 52 70        73 10 18 39 84 9 61 72 50 81 23 83 49 76 29 88 69 74 75 46 82 85        65 78 79 86 89 90];    -   (b) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26        24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 51 47 44 42 38        36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 70 52 16 12 3 73        39 18 10 84 61 9 72 50 81 23 83 49 76 29 88 69 74 75 46 82 85 65        86 79 78 89 90];    -   (c) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 47        51 55 59 62 64 66 77 2 11 25 34 35 43 45 56 71 80 3 9 10 12 16        18 23 29 39 46 49 50 52 61 65 69 70 72 73 74 75 76 78 79 81 82        83 84 85 86 88 89 90];    -   (d) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26        24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 51 47 44 42 38        36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 3 9 10 12 16 18        23 29 39 46 49 50 52 61 65 69 70 72 73 74 75 76 78 79 81 82 83        84 85 86 88 89 90];    -   (e) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 47        51 55 59 62 64 66 77 2 11 25 34 35 43 45 56 71 80 3 12 16 52 70        73 9 10 18 23 29 39 46 49 50 61 65 69 72 74 75 76 78 79 81 82 83        84 85 86 88 89 90];    -   (f) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26        24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 51 47 44 42 38        36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 70 52 16 12 3 73        9 10 18 23 29 39 46 49 50 61 65 69 72 74 75 76 78 79 81 82 83 84        85 86 88 89 90];    -   (g) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 47        51 55 59 62 64 66 77 2 11 25 34 35 43 45 56 71 80 3 12 16 52 70        73 10 18 39 84 9 23 29 46 49 50 61 65 69 72 74 75 76 78 79 81 82        83 85 86 88 89 90];    -   (h) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26        24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 51 47 44 42 38        36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 70 52 16 12 3 73        39 18 10 84 9 23 29 46 49 50 61 65 69 72 74 75 76 78 79 81 82 83        85 86 88 89 90];

5. For high-index bit mapper for K_(max)=140

-   -   (e) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 29 30 37 38        42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111        114 117 119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10        16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118        120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81        94 99 108 113 116 121 124 133 139 146 26 33 34 41 46 77 83 87 88        89 100 101 104 109 110 147 25 51 56 62 76 82 95 140 27 84 86 96        102 161 36 103 105 150 90 159 52 163 63 153 47 143 85 151 158        160 162 35 141 142 148 149 152 154 155 156 157];    -   (f) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 29 30 37 38        42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111        114 117 119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10        16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118        120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81        94 99 108 113 116 121 124 133 139 146 25 26 27 33 34 35 36 41 46        47 51 52 56 62 63 76 77 82 83 84 85 86 87 88 89 90 95 96 100 101        102 103 104 105 109 110 140 141 142 143 147 148 149 150 151 152        153 154 155 156 157 158 159 160 161 162 163];    -   (g) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 29 30 37 38        42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111        114 117 119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10        16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118        120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81        94 99 108 113 116 121 124 133 139 146 26 33 34 41 46 77 83 87 88        89 100 101 104 109 110 147 25 27 35 36 47 51 52 56 62 63 76 82        84 85 86 90 95 96 102 103 105 140 141 142 143 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (h) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 29 30 37 38        42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111        114 117 119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10        16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118        120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81        94 99 108 113 116 121 124 133 139 146 26 33 34 41 46 77 83 87 88        89 100 101 104 109 110 147 25 51 56 62 76 82 95 140 27 35 36 47        52 63 84 85 86 90 96 102 103 105 141 142 143 148 149 150 151 152        153 154 155 156 157 158 159 160 161 162 163];    -   (i) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 17 23 37 48 75        80 86 137 143 13 18 38 144 39 145 40 146 41 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (j) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 17 18 23 37        38 39 40 41 48 75 80 86 137 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (k) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 17 23 37 48 75        80 86 137 143 13 18 38 39 40 41 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (l) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 17 23 37 48 75        80 86 137 143 13 18 38 144 39 40 41 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (m) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 17 23 37 48 75        80 86 137 143 13 18 38 144 39 145 40 41 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (n) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39        80 137 145 17 40 75 146 48 149 37 86 143 144 41 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (o) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 17 18 23 37        38 39 40 41 48 75 80 86 137 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (p) ϕ_(PT)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39        80 137 145 17 37 40 41 48 75 86 143 144 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (q) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39        80 137 145 17 40 75 146 37 41 48 86 143 144 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (r) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51        53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88        89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122        123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35        43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109        112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44        47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39        80 137 145 17 40 75 146 48 149 37 41 86 143 144 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (s) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 38 39        41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85        86 91 98 99 102 106 108 109 111 112 113 115 117 119 120 124 125        126 131 132 133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57        60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122 129 130        136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105        121 127 147 13 26 36 54 73 75 89 92 135 146 14 32 80 88 145 68        69 128 152 1 6 20 78 151 22 83 148 149 123 141 45 140 70 153 154        110 142 143 150 156 157 158];    -   (t) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 38 39        41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85        86 91 98 99 102 106 108 109 111 112 113 115 117 119 120 124 125        126 131 132 133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57        60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122 129 130        136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105        121 127 147 1 6 13 14 20 22 26 32 36 45 54 68 69 70 73 75 78 80        83 88 89 92 110 123 128 135 140 141 142 143 145 146 148 149 150        151 152 153 154 156 157 158];    -   (u) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 38 39        41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85        86 91 98 99 102 106 108 109 111 112 113 115 117 119 120 124 125        126 131 132 133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57        60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122 129 130        136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105        121 127 147 13 26 36 54 73 75 89 92 135 146 1 6 14 20 22 32 45        68 69 70 78 80 83 88 110 123 128 140 141 142 143 145 148 149 150        151 152 153 154 156 157 158];    -   (v) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 38 39        41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85        86 91 98 99 102 106 108 109 111 112 113 115 117 119 120 124 125        126 131 132 133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57        60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122 129 130        136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105        121 127 147 13 26 36 54 73 75 89 92 135 146 14 32 80 88 145 1 6        20 22 45 68 69 70 78 83 110 123 128 140 141 142 143 148 149 150        151 152 153 154 156 157 158];

6. For low-index bit mapper for K_(max)=140

-   -   (i) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 144 1 4        7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108        116 119 123 129 132 135 138 145 0 6 15 18 23 26 31 40 45 58 64        71 78 84 89 94 99 107 115 131 134 137 146 29 30 35 38 39 50 51        52 56 62 93 98 105 106 113 147 44 57 63 77 83 88 114 140 37 43        53 55 112 161 34 36 103 150 49 159 87 163 76 153 92 143 54 151        158 160 162 104 141 142 148 149 152 154 155 156 157];    -   (j) ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118        117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66        61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 144 138        135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41        32 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84        78 71 64 58 45 40 31 26 23 18 15 6 0 146 113 106 105 98 93 62 56        52 51 50 39 38 35 30 29 147 114 88 83 77 63 57 44 140 112 55 53        43 37 161 103 36 34 150 49 159 87 163 76 153 92 143 54 151 158        160 162 104 141 142 148 149 152 154 155 156 157];    -   (k) [2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66        67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111 117 118        120 121 122 124 125 126 127 128 130 133 136 139 144 1 4 7 10 16        19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119        123 129 132 135 138 145 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 146 29 30 34 35 36 37 38 39 43 44        49 50 51 52 53 54 55 56 57 62 63 76 77 83 87 88 92 93 98 103 104        105 106 112 113 114 140 141 142 143 147 148 149 150 151 152 153        154 155 156 157 158 159 160 161 162 163];    -   (l) ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118        117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66        61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 144 138        135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41        32 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84        78 71 64 58 45 40 31 26 23 18 15 6 0 146 114 113 112 106 105 104        103 98 93 92 88 87 83 77 76 63 62 57 56 55 54 53 52 51 50 49 44        43 39 38 37 36 35 34 30 29 140 141 142 143 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (m) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 144 1 4        7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108        116 119 123 129 132 135 138 145 0 6 15 18 23 26 31 40 45 58 64        71 78 84 89 94 99 107 115 131 134 137 146 29 30 35 38 39 50 51        52 56 62 93 98 105 106 113 147 34 36 37 43 44 49 53 54 55 57 63        76 77 83 87 88 92 103 104 112 114 140 141 142 143 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (n) ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118        117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66        61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 144 138        135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41        32 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84        78 71 64 58 45 40 31 26 23 18 15 6 0 146 113 106 105 98 93 62 56        52 51 50 39 38 35 30 29 147 114 112 104 103 92 88 87 83 77 76 63        57 55 54 53 49 44 43 37 36 34 140 141 142 143 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (o) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 144 1 4        7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108        116 119 123 129 132 135 138 145 0 6 15 18 23 26 31 40 45 58 64        71 78 84 89 94 99 107 115 131 134 137 146 29 30 35 38 39 50 51        52 56 62 93 98 105 106 113 147 44 57 63 77 83 88 114 140 34 36        37 43 49 53 54 55 76 87 92 103 104 112 141 142 143 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (p) ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118        117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66        61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 144 138        135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41        32 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84        78 71 64 58 45 40 31 26 23 18 15 6 0 146 113 106 105 98 93 62 56        52 51 50 39 38 35 30 29 147 114 88 83 77 63 57 44 140 112 104        103 92 87 76 55 54 53 49 43 37 36 34 141 142 143 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (q) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 102 116 122        127 143 101 121 126 144 100 145 99 146 98 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (r) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64        59 53 2 143 126 121 101 144 100 145 99 146 98 147 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (s) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 98 99 100        101 102 116 121 122 126 127 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (t) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 2 53 59 64 91 98 99 100        101 102 116 121 122 126 127 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (u) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 102 116 122        127 143 98 99 100 101 121 126 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (v) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64        59 53 2 143 98 99 100 101 121 126 144 145 146 147 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (w) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 102 116 122        127 143 101 121 126 144 98 99 100 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (x) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64        59 53 2 143 126 121 101 144 98 99 100 145 146 147 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (y) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 102 116 122        127 143 101 121 126 144 100 145 98 99 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (z) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64        59 53 2 143 126 121 101 144 100 145 98 99 146 147 148 149 150        151 152 153 154 155 156 157 158 159 160 161 162 163];    -   (aa) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126        127 145 64 99 122 146 91 149 53 102 143 144 98 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (bb) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100        59 2 145 122 99 64 146 91 149 102 53 143 144 98 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (cc) ϕ_(T)-[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 53 59 64 91 98 99 100        101 102 116 121 122 126 127 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (dd) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 2 53 59 64 91 98 99 100        101 102 116 121 122 126 127 143 144 145 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (ee) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126        127 145 53 64 91 98 99 102 122 143 144 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (ff) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100        59 2 145 53 64 91 98 99 102 122 143 144 146 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (gg) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126        127 145 64 99 122 146 53 91 98 102 143 144 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (hh) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100        59 2 145 122 99 64 146 53 91 98 102 143 144 147 148 149 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (ii) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37        40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112        118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75        92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126        127 145 64 99 122 146 91 149 53 98 102 143 144 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (jj) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108        105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63        62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20        19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112        110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37        34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103        95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100        59 2 145 122 99 64 146 91 149 53 98 102 143 144 147 148 150 151        152 153 154 155 156 157 158 159 160 161 162 163];    -   (kk) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 72 73 77 80 81 83 84 86 87 88        91 92 97 98 100 101 102 104 106 111 114 115 116 120 121 123 127        128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 25 32 35 36 43        49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124 130        132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112        131 147 4 47 50 64 66 85 103 113 126 146 51 59 107 125 145 11 70        71 152 61 119 133 138 151 56 117 148 149 16 141 94 140 69 153        154 29 142 143 150 156 157 158];    -   (ll) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116 115 114        111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 73        72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22        20 19 15 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99        96 95 93 82 79 78 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9        3 2 1 144 131 112 108 105 90 89 74 65 46 45 44 42 39 38 34 18 12        147 126 113 103 85 66 64 50 47 4 146 125 107 59 51 145 71 70 11        152 138 133 119 61 151 117 56 148 149 16 141 94 140 69 153 154        29 143 142 150 156 157 158];    -   (mm) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 72 73 77 80 81 83 84 86 87 88        91 92 97 98 100 101 102 104 106 111 114 115 116 120 121 123 127        128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 25 32 35 36 43        49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124 130        132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112        131 147 4 11 16 29 47 50 51 56 59 61 64 66 69 70 71 85 94 103        107 113 117 119 125 126 133 138 140 141 142 143 145 146 148 149        150 151 152 153 154 156 157 158];    -   (nn) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116 115 114        111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 73        72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22        20 19 15 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99        96 95 93 82 79 78 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9        3 2 1 144 131 112 108 105 90 89 74 65 46 45 44 42 39 38 34 18 12        147 4 11 16 29 47 50 51 56 59 61 64 66 69 70 71 85 94 103 107        113 117 119 125 126 133 138 140 141 142 143 145 146 148 149 150        151 152 153 154 156 157 158];    -   (oo) ϕ_(T)-[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 72 73 77 80 81 83 84 86 87 88        91 92 97 98 100 101 102 104 106 111 114 115 116 120 121 123 127        128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 25 32 35 36 43        49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124 130        132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112        131 147 4 47 50 64 66 85 103 113 126 146 11 16 29 51 56 59 61 69        70 71 94 107 117 119 125 133 138 140 141 142 143 145 148 149 150        151 152 153 154 156 157 158];    -   (pp) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116 115 114        111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 73        72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22        20 19 15 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99        96 95 93 82 79 78 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9        3 2 1 144 131 112 108 105 90 89 74 65 46 45 44 42 39 38 34 18 12        147 126 113 103 85 66 64 50 47 4 146 11 16 29 51 56 59 61 69 70        71 94 107 117 119 125 133 138 140 141 142 143 145 148 149 150        151 152 153 154 156 157 158 ];    -   (qq) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37        40 41 48 53 54 57 58 60 63 67 68 72 73 77 80 81 83 84 86 87 88        91 92 97 98 100 101 102 104 106 111 114 115 116 120 121 123 127        128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 25 32 35 36 43        49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124 130        132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112        131 147 4 47 50 64 66 85 103 113 126 146 51 59 107 125 145 11 16        29 56 61 69 70 71 94 117 119 133 138 140 141 142 143 148 149 150        151 152 153 154 156 157 158];    -   (rr) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116 115 114        111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 73        72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22        20 19 15 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99        96 95 93 82 79 78 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9        3 2 1 144 131 112 108 105 90 89 74 65 46 45 44 42 39 38 34 18 12        147 126 113 103 85 66 64 50 47 4 146 125 107 59 51 145 11 16 29        56 61 69 70 71 94 117 119 133 138 140 141 142 143 148 149 150        151 152 153 154 156 157 158];

7. For high-index bit mapper for K_(max)=160

-   -   (a) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 37 43 57 68 95 100 106 157 163 33 38 58 164 59 165 60 166 61        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (b) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38        39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93        98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150        151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64        69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152        155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114        119 128 133 136 141 144 153 159 166 46 53 54 61 66 97 103 107        108 109 120 121 124 129 130 167 10 15 45 71 76 82 96 102 115 160        11 47 104 106 116 122 181 56 123 125 170 110 179 72 183 83 173        67 163 105 171 178 180 182 55 161 162 168 169 172 174 175 176        177];    -   (c) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 37 38 43 57 58 59 60 61 68 95 100 106 157 163 164 165 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (d) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38        39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93        98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150        151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64        69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152        155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114        119 128 133 136 141 144 153 159 166 10 11 15 45 46 47 53 54 55        56 61 66 67 71 72 76 82 83 96 97 102 103 104 105 106 107 108 109        110 115 116 120 121 122 123 124 125 129 130 160 161 162 163 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (e) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 37 43 57 68 95 100 106 157 163 33 38 58 59 60 61 164 165 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (f) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38        39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93        98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150        151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64        69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152        155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114        119 128 133 136 141 144 153 159 166 46 53 54 61 66 97 103 107        108 109 120 121 124 129 130 167 10 11 15 45 47 55 56 67 71 72 76        82 83 96 102 104 105 106 110 115 116 122 123 125 160 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (g) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 37 43 57 68 95 100 106 157 163 33 38 58 164 59 60 61 165 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (h) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38        39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93        98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150        151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64        69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152        155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114        119 128 133 136 141 144 153 159 166 46 53 54 61 66 97 103 107        108 109 120 121 124 129 130 167 10 15 45 71 76 82 96 102 115 160        11 47 55 56 67 72 83 104 105 106 110 116 122 123 125 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (i) ϕ_(PT)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 37 43 57 68 95 100 106 157 163 33 38 58 164 59 165 60 61 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (j) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38        39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93        98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150        151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64        69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152        155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114        119 128 133 136 141 144 153 159 166 46 53 54 61 66 97 103 107        108 109 120 121 124 129 130 167 10 15 45 71 76 82 96 102 115 160        11 47 104 106 116 122 181 55 56 67 72 83 105 110 123 125 161 162        163 168 169 170 171 172 173 174 175 176 177 178 179 180 182        183];    -   (k) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 38 43 58 59 100 157 165 37 60 95 166 68 169 57 106 163 164        61 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (l) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 37 38 43 57 58 59 60 61 68 95 100 106 157 163 164 165 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (m) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 38 43 58 59 100 157 165 37 57 60 61 68 95 106 163 164 166        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (n) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 38 43 58 59 100 157 165 37 60 95 166 57 61 68 106 163 164        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (o) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40        44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87        89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121        124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152        154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55        63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125        127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42        50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13        32 33 38 43 58 59 100 157 165 37 60 95 166 68 169 57 61 106 163        164 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182        183];

8. For low-index bit mapper for K_(max)=160

-   -   (a) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91        102 116 122 127 146 163 101 121 126 164 100 165 99 166 98 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (b) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 59        65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140        142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 145 150 157 166 29 30 35 38 39 50        51 52 56 62 93 98 105 106 113 167 44 57 63 77 83 88 114 144 149        160 37 43 53 55 112 148 181 34 36 103 170 49 179 87 183 76 173        92 163 54 171 178 180 182 104 161 162 168 169 172 174 175 176        177];    -   (c) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122        116 102 91 64 59 53 2 163 126 121 101 164 100 165 99 166 98 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (d) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128        127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91        86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17        14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132        129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27        24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94        89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 93        62 56 52 51 50 39 38 35 30 29 167 149 144 114 88 83 77 63 57 44        160 148 112 55 53 43 37 181 103 36 34 170 49 179 87 183 76 173        92 163 54 171 178 180 182 104 161 162 168 169 172 174 175 176        177];    -   (e) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91 98        99 100 101 102 116 121 122 126 127 146 163 164 165 166 167 168        169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (f) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 59        65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140        142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 145 150 157 166 29 30 34 35 36 37        38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77 83 87 88 92        93 98 103 104 105 106 112 113 114 144 148 149 160 161 162 163        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (g) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 2 53 59 64        91 98 99 100 101 102 116 121 122 126 127 146 163 164 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (h) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128        127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91        86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17        14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132        129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27        24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94        89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 29 30 34 35 36 37        38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77 83 87 88 92        93 98 103 104 105 106 112 113 114 144 148 149 160 161 162 163        167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (i) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91        102 116 122 127 146 163 98 99 100 101 121 126 164 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (j) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 59        65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140        142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 145 150 157 166 29 30 35 38 39 50        51 52 56 62 93 98 105 106 113 167 34 36 37 43 44 49 53 54 55 57        63 76 77 83 87 88 92 103 104 112 114 144 148 149 160 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (k) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122        116 102 91 64 59 53 2 163 98 99 100 101 121 126 164 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (l) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128        127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91        86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17        14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132        129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27        24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94        89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 93        62 56 52 51 50 39 38 35 30 29 167 34 36 37 43 44 49 53 54 55 57        63 76 77 83 87 88 92 103 104 112 114 144 148 149 160 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (m) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91        102 116 122 127 146 163 101 121 126 164 98 99 100 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (n) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 59        65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140        142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 145 150 157 166 29 30 35 38 39 50        51 52 56 62 93 98 105 106 113 167 44 57 63 77 83 88 114 144 149        160 34 36 37 43 49 53 54 55 76 87 92 103 104 112 148 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (o) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122        116 102 91 64 59 53 2 163 126 121 101 164 98 99 100 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (p) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128        127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91        86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17        14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132        129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27        24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94        89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 93        62 56 52 51 50 39 38 35 30 29 167 149 144 114 88 83 77 63 57 44        160 34 36 37 43 49 53 54 55 76 87 92 103 104 112 148 161 162 163        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (q) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91        102 116 122 127 146 163 101 121 126 164 100 165 98 99 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (r) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 59        65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140        142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84        89 94 99 107 115 131 134 137 145 150 157 166 29 30 35 38 39 50        51 52 56 62 93 98 105 106 113 167 44 57 63 77 83 88 114 144 149        160 37 43 53 55 112 148 181 34 36 49 54 76 87 92 103 104 161 162        163 168 169 170 171 172 173 174 175 176 177 178 179 180 182        183];    -   (s) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122        116 102 91 64 59 53 2 163 126 121 101 164 100 165 98 99 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (t) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128        127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91        86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17        14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132        129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27        24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94        89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 93        62 56 52 51 50 39 38 35 30 29 167 149 144 114 88 83 77 63 57 44        160 148 112 55 53 43 37 181 34 36 49 54 76 87 92 103 104 161 162        163 168 169 170 171 172 173 174 175 176 177 178 179 180 182        183];    -   (u) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 59 100 101 116        121 126 127 146 165 64 99 122 166 91 169 53 102 163 164 98 167        168 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (v) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 59 100 101 116        121 126 127 146 165 64 99 122 166 91 169 53 102 163 164 98 167        168 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (w) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 126        121 116 101 100 59 2 165 122 99 64 166 91 169 102 53 163 164 98        167 168 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (x) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91 98        99 100 101 102 116 121 122 126 127 146 163 164 165 166 167 168        169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (y) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 2 53 59 64        91 98 99 100 101 102 116 121 122 126 127 146 163 164 165 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (z) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 59 100 101 116        121 126 127 146 165 53 64 91 98 99 102 122 163 164 166 167 168        169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (aa) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 126        121 116 101 100 59 2 165 53 64 91 98 99 102 122 163 164 166 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (bb) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 59 100 101 116        121 126 127 146 165 64 99 122 166 53 91 98 102 163 164 167 168        169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (cc) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 126        121 116 101 100 59 2 165 122 99 64 166 53 91 98 102 163 164 167        168 169 170 171 172 173 174 175 176 177 178 179 180 181 182        183];    -   (dd) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49        55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131        134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60        65 75 92 95 103 106 109 117 123 128 133 147 162 2 59 100 101 116        121 126 127 146 165 64 99 122 166 91 169 53 98 102 163 164 167        168 170 171 172 173 174 175 176 177 178 179 180 181 182 183];    -   (ee) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139        137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89        88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52        51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12        10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117        109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 126        121 116 101 100 59 2 165 122 99 64 166 91 169 53 98 102 163 164        167 168 170 171 172 173 174 175 176 177 178 179 180 181 182        183];

9. For high-index bit mapper for K_(max)=200

-   -   (a) ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39        40 43 44 45 47 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81        82 88 89 90 97 98 102 103 108 113 117 119 124 125 126 129 131        132 133 138 139 151 152 157 166 171 174 177 179 182 185 186 187        188 190 191 194 196 197 204 4 11 13 17 22 24 28 30 32 35 37 41        46 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118 120        127 130 134 140 153 158 167 172 175 178 180 183 189 192 195 198        205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121        128 135 141 154 159 168 173 176 181 184 193 199 206 8 15 86 93        94 101 106 137 143 147 148 149 160 161 164 169 170 207 6 19 50        55 85 111 116 122 136 142 155 200 87 95 107 144 150 162 165 208        51 156 214 7 146 221 163 219 96 210 145 202 212 112 211 216 223        123 201 203 209 213 215 217 218 220 222];    -   (b) ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39        40 43 44 45 47 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81        82 88 89 90 97 98 102 103 108 113 117 119 124 125 126 129 131        132 133 138 139 151 152 157 166 171 174 177 179 182 185 186 187        188 190 191 194 196 197 204 4 11 13 17 22 24 28 30 32 35 37 41        46 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118 120        127 130 134 140 153 158 167 172 175 178 180 183 189 192 195 198        205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121        128 135 141 154 159 168 173 176 181 184 193 199 206 6 7 8 15 19        50 51 55 85 86 87 93 94 95 96 101 106 107 111 112 116 122 123        136 137 142 143 144 145 146 147 148 149 150 155 156 160 161 162        163 164 165 169 170 200 201 202 203 207 208 209 210 211 212 213        214 215 216 217 218 219 220 221 222 223];    -   (c) ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39        40 43 44 45 47 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81        82 88 89 90 97 98 102 103 108 113 117 119 124 125 126 129 131        132 133 138 139 151 152 157 166 171 174 177 179 182 185 186 187        188 190 191 194 196 197 204 4 11 13 17 22 24 28 30 32 35 37 41        46 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118 120        127 130 134 140 153 158 167 172 175 178 180 183 189 192 195 198        205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121        128 135 141 154 159 168 173 176 181 184 193 199 206 8 15 86 93        94 101 106 137 143 147 148 149 160 161 164 169 170 207 6 7 19 50        51 55 85 87 95 96 107 111 112 116 122 123 136 142 144 145 146        150 155 156 162 163 165 200 201 202 203 208 209 210 211 212 213        214 215 216 217 218 219 220 221 222 223];    -   (d) ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39        40 43 44 45 47 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81        82 88 89 90 97 98 102 103 108 113 117 119 124 125 126 129 131        132 133 138 139 151 152 157 166 171 174 177 179 182 185 186 187        188 190 191 194 196 197 204 4 11 13 17 22 24 28 30 32 35 37 41        46 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118 120        127 130 134 140 153 158 167 172 175 178 180 183 189 192 195 198        205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121        128 135 141 154 159 168 173 176 181 184 193 199 206 8 15 86 93        94 101 106 137 143 147 148 149 160 161 164 169 170 207 6 19 50        55 85 111 116 122 136 142 155 200 7 51 87 95 96 107 112 123 144        145 146 150 156 162 163 165 201 202 203 208 209 210 211 212 213        214 215 216 217 218 219 220 221 222 223];    -   (e) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 77 83 97 108 135 140 146 197 203 73        78 98 204 99 205 100 206 101 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (f) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 73 77 78 83 97 98 99 100 101 108 135        140 146 197 203 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (g) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 77 83 97 108 135 140 146 197 203 73        78 98 99 100 101 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (h) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 77 83 97 108 135 140 146 197 203 73        78 98 204 99 100 101 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (i) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 77 83 97 108 135 140 146 197 203 73        78 98 204 99 205 100 101 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (j) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77 100        135 206 108 209 97 146 203 204 101 207 208 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (k) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 31 53 72 73 77 78 83 97 98 99 100 101 108 135        140 146 197 203 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (l) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77 97 100        101 108 135 146 203 204 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (m) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77 100        135 206 97 101 108 146 203 204 207 208 209 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (n) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38        39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80        84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121        122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149        151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182        183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34        36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106        112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165        167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30        52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177        185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77 100        135 206 108 209 97 101 146 203 204 207 208 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (o) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 31 34 41 42 47        52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 97 98        99 102 103 104 106 108 109 110 114 116 118 120 121 122 123 125        128 129 132 135 137 141 142 144 148 152 156 158 160 161 162 163        164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194        196 197 212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62        65 84 88 93 95 101 107 111 112 113 115 119 126 127 131 136 139        145 146 151 159 168 169 173 175 184 185 186 193 199 215 3 10 14        16 23 29 30 37 40 43 55 56 67 75 77 81 100 117 124 147 150 167        176 182 190 198 204 33 44 87 91 94 134 153 154 155 157 165 207        53 61 66 80 138 195 211 82 96 105 140 143 170 218 6 39 86 92 208        15 22 183 200 49 130 210 149 203 48 202 59 201 209 214 133 205        206 213 216 217];    -   (p) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 31 34 41 42 47        52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 97 98        99 102 103 104 106 108 109 110 114 116 118 120 121 122 123 125        128 129 132 135 137 141 142 144 148 152 156 158 160 161 162 163        164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194        196 197 212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62        65 84 88 93 95 101 107 111 112 113 115 119 126 127 131 136 139        145 146 151 159 168 169 173 175 184 185 186 193 199 215 3 10 14        16 23 29 30 37 40 43 55 56 67 75 77 81 100 117 124 147 150 167        176 182 190 198 204 6 15 22 33 39 44 48 49 53 59 61 66 80 82 86        87 91 92 94 96 105 130 133 134 138 140 143 149 153 154 155 157        165 170 183 195 200 201 202 203 205 206 207 208 209 210 211 213        214 216 217 218];    -   (q) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 31 34 41 42 47        52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 97 98        99 102 103 104 106 108 109 110 114 116 118 120 121 122 123 125        128 129 132 135 137 141 142 144 148 152 156 158 160 161 162 163        164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194        196 197 212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62        65 84 88 93 95 101 107 111 112 113 115 119 126 127 131 136 139        145 146 151 159 168 169 173 175 184 185 186 193 199 215 3 10 14        16 23 29 30 37 40 43 55 56 67 75 77 81 100 117 124 147 150 167        176 182 190 198 204 33 44 87 91 94 134 153 154 155 157 165 207 6        15 22 39 48 49 53 59 61 66 80 82 86 92 96 105 130 133 138 140        143 149 170 183 195 200 201 202 203 205 206 208 209 210 211 213        214 216 217 218];    -   (r) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 31 34 41 42 47        52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 97 98        99 102 103 104 106 108 109 110 114 116 118 120 121 122 123 125        128 129 132 135 137 141 142 144 148 152 156 158 160 161 162 163        164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194        196 197 212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62        65 84 88 93 95 101 107 111 112 113 115 119 126 127 131 136 139        145 146 151 159 168 169 173 175 184 185 186 193 199 215 3 10 14        16 23 29 30 37 40 43 55 56 67 75 77 81 100 117 124 147 150 167        176 182 190 198 204 33 44 87 91 94 134 153 154 155 157 165 207        53 61 66 80 138 195 211 6 15 22 39 48 49 59 82 86 92 96 105 130        133 140 143 149 170 183 200 201 202 203 205 206 208 209 210 213        214 216 217 218];

10. For low-index bit mapper for K_(max)=200

-   -   (a) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 160 161 163 165 168 170 172 173 176 178        179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 24 27        32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132        135 138 140 142 146 151 153 158 162 164 167 169 171 175 177 182        186 188 195 205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99        107 115 131 134 137 145 150 157 166 174 181 185 194 206 29 30 35        38 39 50 51 52 56 62 93 98 105 106 113 184 191 207 44 57 63 77        83 88 114 144 149 180 193 200 34 37 49 55 92 104 112 208 43 148        214 53 192 221 36 219 103 210 54 202 212 87 211 216 223 76 201        203 209 213 215 217 218 220 222];    -   (b) ϕ_(T)=[199 198 197 196 190 189 187 183 179 178 176 173 172        170 168 165 163 161 160 159 156 155 154 152 147 143 141 139 136        133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102        101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28        25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177 175        171 169 167 164 162 158 153 151 146 142 140 138 135 132 129 123        119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19        16 10 7 4 1 205 194 185 181 174 166 157 150 145 137 134 131 115        107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 206 191 184        113 106 105 98 93 62 56 52 51 50 39 38 35 30 29 207 193 180 149        144 114 88 83 77 63 57 44 200 112 104 92 55 49 37 34 208 148 43        214 192 53 221 36 219 103 210 54 212 202 87 211 216 223 76 215        213 217 218 201 220 203 222 209];    -   (c) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 160 161 163 165 168 170 172 173 176 178        179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 24 27        32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132        135 138 140 142 146 151 153 158 162 164 167 169 171 175 177 182        186 188 195 205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99        107 115 131 134 137 145 150 157 166 174 181 185 194 206 29 30 34        35 36 37 38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77 83        87 88 92 93 98 103 104 105 106 112 113 114 144 148 149 180 184        191 192 193 200 201 202 203 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (d) ϕ_(T)=[199 198 197 196 190 189 187 183 179 178 176 173 172        170 168 165 163 161 160 159 156 155 154 152 147 143 141 139 136        133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102        101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28        25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177 175        171 169 167 164 162 158 153 151 146 142 140 138 135 132 129 123        119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19        16 10 7 4 1 205 194 185 181 174 166 157 150 145 137 134 131 115        107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 206 29 30        34 35 36 37 38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77        83 87 88 92 93 98 103 104 105 106 112 113 114 144 148 149 180        184 191 192 193 200 201 202 203 207 208 209 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (e) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 160 161 163 165 168 170 172 173 176 178        179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 24 27        32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132        135 138 140 142 146 151 153 158 162 164 167 169 171 175 177 182        186 188 195 205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99        107 115 131 134 137 145 150 157 166 174 181 185 194 206 29 30 35        38 39 50 51 52 56 62 93 98 105 106 113 184 191 207 34 36 37 43        44 49 53 54 55 57 63 76 77 83 87 88 92 103 104 112 114 144 148        149 180 192 193 200 201 202 203 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (f) ϕ_(T)=[199 198 197 196 190 189 187 183 179 178 176 173 172        170 168 165 163 161 160 159 156 155 154 152 147 143 141 139 136        133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102        101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28        25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177 175        171 169 167 164 162 158 153 151 146 142 140 138 135 132 129 123        119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19        16 10 7 4 1 205 194 185 181 174 166 157 150 145 137 134 131 115        107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 206 191 184        113 106 105 98 93 62 56 52 51 50 39 38 35 30 29 207 34 36 37 43        44 49 53 54 55 57 63 76 77 83 87 88 92 103 104 112 114 144 148        149 180 192 193 200 201 202 203 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (g) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60        61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111        117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143        147 152 154 155 156 159 160 161 163 165 168 170 172 173 176 178        179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 24 27        32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132        135 138 140 142 146 151 153 158 162 164 167 169 171 175 177 182        186 188 195 205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99        107 115 131 134 137 145 150 157 166 174 181 185 194 206 29 30 35        38 39 50 51 52 56 62 93 98 105 106 113 184 191 207 44 57 63 77        83 88 114 144 149 180 193 200 34 36 37 43 49 53 54 55 76 87 92        103 104 112 148 192 201 202 203 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (h) ϕ_(T)=[199 198 197 196 190 189 187 183 179 178 176 173 172        170 168 165 163 161 160 159 156 155 154 152 147 143 141 139 136        133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102        101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28        25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177 175        171 169 167 164 162 158 153 151 146 142 140 138 135 132 129 123        119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19        16 10 7 4 1 205 194 185 181 174 166 157 150 145 137 134 131 115        107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 206 191 184        113 106 105 98 93 62 56 52 51 50 39 38 35 30 29 207 193 180 149        144 114 88 83 77 63 57 44 200 34 36 37 43 49 53 54 55 76 87 92        103 104 112 148 192 201 202 203 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (i) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 102 116 122 127 146 168 172 203 101        121 126 204 100 205 99 206 98 207 208 209 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (j) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 168 146 127 122 116 102 91 64 59 53 2 203 126 121        101 204 100 205 99 206 98 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (k) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127        146 168 172 203 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (l) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 146        168 172 203 204 205 206 207 208 209 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (m) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 102 116 122 127 146 168 172 203 98 99        100 101 121 126 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (n) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 168 146 127 122 116 102 91 64 59 53 2 203 98 99 100        101 121 126 204 205 206 207 208 209 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (o) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 102 116 122 127 146 168 172 203 101        121 126 204 98 99 100 205 206 207 208 209 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (p) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 168 146 127 122 116 102 91 64 59 53 2 203 126 121        101 204 98 99 100 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (q) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 102 116 122 127 146 168 172 203 101        121 126 204 100 205 98 99 206 207 208 209 210 211 212 213 214        215 216 217 218 219 220 221 222 223];    -   (r) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 168 146 127 122 116 102 91 64 59 53 2 203 126 121        101 204 100 205 98 99 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (s) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 59 100 101 116 121 126 127 146 172 205 64 99 122        168 206 91 209 53 102 203 204 98 207 208 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (t) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 146 127 126 121 116 101 100 59 2 205 168 122 99 64        206 91 209 102 53 203 204 98 207 208 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (u) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127        146 168 172 203 204 205 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (v) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 146        168 172 203 204 205 206 207 208 209 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (w) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 59 100 101 116 121 126 127 146 172 205 53 64 91 98        99 102 122 168 203 204 206 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (x) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 146 127 126 121 116 101 100 59 2 205 53 64 91 98 99        102 122 168 203 204 206 207 208 209 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (y) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 59 100 101 116 121 126 127 146 172 205 64 99 122        168 206 53 91 98 102 203 204 207 208 209 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (z) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 146 127 126 121 116 101 100 59 2 205 168 122 99 64        206 53 91 98 102 203 204 207 208 209 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (aa) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35        38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77        78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120        125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157        158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187        188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34        37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110        112 118 124 129 131 134 136 138 141 143 148 151 154 156 163 165        170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42        54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181        184 189 202 2 59 100 101 116 121 126 127 146 172 205 64 99 122        168 206 91 209 53 98 102 203 204 207 208 210 211 212 213 214 215        216 217 218 219 220 221 222 223];    -   (bb) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177        175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149        145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111        108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67        63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21        20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176        174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124        118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43        40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169        147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14        8 3 202 172 146 127 126 121 116 101 100 59 2 205 168 122 99 64        206 91 209 53 98 102 203 204 207 208 210 211 212 213 214 215 216        217 218 219 220 221 222 223];    -   (cc) ϕ_(T)=[2, 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36        37 38 39 41 43 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81        83 85 89 90 91 93 95 96 97 100 101 102 109 110 114 116 120 121        123 125 126 127 128 129 130 131 135 136 142 145 147 152 157 158        165 168 171 173 175 178 180 181 182 187 188 190 194 195 198 199        212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 80 84 86        87 88 92 98 104 106 111 115 134 137 139 141 148 149 153 154 161        163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 49 52        75 82 99 118 122 124 132 143 144 156 159 162 169 170 176 183 185        189 196 204 34 42 44 45 46 65 105 108 112 155 166 207 4 61 119        133 138 146 211 29 56 59 94 103 117 218 107 113 160 193 208 16        177 184 200 69 150 210 50 203 151 202 140 201 209 214 66 205 206        213 216 217];    -   (dd) ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173        171 168 165 158 157 152 147 145 142 136 135 131 130 129 128 127        126 125 123 121 120 116 114 110 109 102 101 100 97 96 95 93 91        90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 58 57 55 51 47 43        41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 7 5 3 2        212 197 192 191 186 179 174 172 167 164 163 161 154 153 149 148        141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63        60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176        170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 49 32 23        17 9 1 204 166 155 112 108 105 65 46 45 44 42 34 207 146 138 133        119 61 4 211 117 103 94 59 56 29 218 193 160 113 107 208 184 177        16 200 150 69 210 50 203 151 202 140 209 214 201 66 206 213 216        217 205];    -   (ee) ϕ_(T)=[2, 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36        37 38 39 41 43 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81        83 85 89 90 91 93 95 96 97 100 101 102 109 110 114 116 120 121        123 125 126 127 128 129 130 131 135 136 142 145 147 152 157 158        165 168 171 173 175 178 180 181 182 187 188 190 194 195 198 199        212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 80 84 86        87 88 92 98 104 106 111 115 134 137 139 141 148 149 153 154 161        163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 49 52        75 82 99 118 122 124 132 143 144 156 159 162 169 170 176 183 185        189 196 204 4 16 29 34 42 44 45 46 50 56 59 61 65 66 69 94 103        105 107 108 112 113 117 119 133 138 140 146 150 151 155 160 166        177 184 193 200 201 202 203 205 206 207 208 209 210 211 213 214        216 217 218];    -   (ff) ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173        171 168 165 158 157 152 147 145 142 136 135 131 130 129 128 127        126 125 123 121 120 116 114 110 109 102 101 100 97 96 95 93 91        90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 58 57 55 51 47 43        41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 7 5 3 2        212 197 192 191 186 179 174 172 167 164 163 161 154 153 149 148        141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63        60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176        170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 49 32 23        17 9 1 204 4 16 29 34 42 44 45 46 50 56 59 61 65 66 69 94 103        105 107 108 112 113 117 119 133 138 140 146 150 151 155 160 166        177 184 193 200 201 202 203 205 206 207 208 209 210 211 213 214        216 217 218];    -   (gg) ϕ_(T)=[2, 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36        37 38 39 41 43 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81        83 85 89 90 91 93 95 96 97 100 101 102 109 110 114 116 120 121        123 125 126 127 128 129 130 131 135 136 142 145 147 152 157 158        165 168 171 173 175 178 180 181 182 187 188 190 194 195 198 199        212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 80 84 86        87 88 92 98 104 106 111 115 134 137 139 141 148 149 153 154 161        163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 49 52        75 82 99 118 122 124 132 143 144 156 159 162 169 170 176 183 185        189 196 204 34 42 44 45 46 65 105 108 112 155 166 207 4 16 29 50        56 59 61 66 69 94 103 107 113 117 119 133 138 140 146 150 151        160 177 184 193 200 201 202 203 205 206 208 209 210 211 213 214        216 217 218];    -   (hh) ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173        171 168 165 158 157 152 147 145 142 136 135 131 130 129 128 127        126 125 123 121 120 116 114 110 109 102 101 100 97 96 95 93 91        90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 58 57 55 51 47 43        41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 7 5 3 2        212 197 192 191 186 179 174 172 167 164 163 161 154 153 149 148        141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63        60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176        170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 49 32 23        17 9 1 204 166 155 112 108 105 65 46 45 44 42 34 207 4 16 29 50        56 59 61 66 69 94 103 107 113 117 119 133 138 140 146 150 151        160 177 184 193 200 201 202 203 205 206 208 209 210 211 213 214        216 217 218];    -   (ii) ϕ_(T)=[2 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36        37 38 39 41 43 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81        83 85 89 90 91 93 95 96 97 100 101 102 109 110 114 116 120 121        123 125 126 127 128 129 130 131 135 136 142 145 147 152 157 158        165 168 171 173 175 178 180 181 182 187 188 190 194 195 198 199        212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 80 84 86        87 88 92 98 104 106 111 115 134 137 139 141 148 149 153 154 161        163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 49 52        75 82 99 118 122 124 132 143 144 156 159 162 169 170 176 183 185        189 196 204 34 42 44 45 46 65 105 108 112 155 166 207 4 61 119        133 138 146 211 16 29 50 56 59 66 69 94 103 107 113 117 140 150        151 160 177 184 193 200 201 202 203 205 206 208 209 210 213 214        216 217 218];    -   (jj) ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173        171 168 165 158 157 152 147 145 142 136 135 131 130 129 128 127        126 125 123 121 120 116 114 110 109 102 101 100 97 96 95 93 91        90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 58 57 55 51 47 43        41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 7 5 3 2        212 197 192 191 186 179 174 172 167 164 163 161 154 153 149 148        141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63        60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176        170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 49 32 23        17 9 1 204 166 155 112 108 105 65 46 45 44 42 34 207 146 138 133        119 61 4 211 16 29 50 56 59 66 69 94 103 107 113 117 140 150 151        160 177 184 193 200 201 202 203 205 206 208 209 210 213 214 216        217 218];    -   (kk) ϕ_(T)=[2, 3, 5, 7, 8, 10, 11, 12, 18, 19, 20, 21, 22, 25,        27, 28, 33, 35, 36, 37, 38, 39, 41, 43, 47, 51, 55, 57, 58, 62,        64, 67, 70, 71, 74, 76, 77, 78, 79, 81, 83, 85, 89, 90, 91, 93,        95, 96, 97, 100, 101, 102, 109, 110, 114, 116, 120, 121, 123,        125, 126, 127, 128, 129, 130, 131, 135, 136, 142, 145, 147, 152,        157, 158, 165, 168, 171, 173, 175, 178, 180, 181, 182, 187, 188,        190, 194, 195, 198, 199, 212, 0, 6, 13, 14, 15, 24, 26, 30, 31,        40, 48, 53, 54, 60, 63, 68, 72, 73, 80, 84, 86, 87, 88, 92, 98,        104, 106, 111, 115, 134, 137, 139, 141, 148, 149, 153, 154, 161,        163, 164, 167, 172, 174, 179, 186, 191, 192, 197, 215, 1, 9, 17,        23, 32, 49, 52, 75, 82, 99, 118, 122, 124, 132, 143, 144, 156,        159, 162, 169, 170, 176, 183, 185, 189, 196, 204, 34, 42, 44,        45, 46, 65, 105, 108, 112, 155, 166, 207, 4, 61, 119, 133, 138,        146, 211, 29, 56, 59, 94, 103, 117, 218, 107, 113, 160, 193,        208, 16, 177, 184, 200, 140, 151, 201, 66, 205, 50, 209, 150,        206, 69, 202, 203, 210, 213, 214, 216, 217];

Particular embodiments include some of the following features andbenefits. In particular embodiments, CRC checking can be done bit-by-bitfor each individual CRC bit. This is in contrast to existing methodswhere the entire length-K_(CRC) vector of CRC bits are used in CRCchecking. Bit-by-bit CRC checking enables the decoder to terminate thedecoding process earlier should the decoded value of any of the CRC bitsbe found to be inconsistent with the decoded values of the informationbits upon which the CRC bits depend, for all candidate paths in thelist. The CRC checking can be performed during the SCL decoding. This isin contrast to existing methods which performs CRC checking only afterthe end of SCL decoding.

In particular embodiments, the decoder at the receiver can be run withthe early termination feature, using the distributed CRC bits. In someembodiments, the distributed CRC bits do not carry a mask. When thedecoder reaches a distributed CRC bit p_(i), the decoder performs thefollowing to decide if the decoding process should terminate early.

Step 1: The decoder calculates L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1.

Step 2: For each p_(i)(

), the decoder checks if the info bits associated with p_(i)(

) results in a successful parity check.

Step 3: if no parity check for each p_(i)(

) are successful, the decoding process can terminate and deliver a‘decoding failure’ message as the decoder output. If parity check(s) forone or more of p_(i)(

) are successful, then the decoding process continues normally.

In another embodiment, the distributed CRC bits carry a mask (i.e., thedistributed CRC bit q_(i), and becomes: w_(i)=(p_(i)+q_(i)) mod 2. Whenthe decoder reaches the bit location of a distributed CRC bit p_(i), thedecoder performs the following to decide if the decoding process shouldterminate early.

Step 1: The decoder calculates L estimated values, w_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1.

Step 2: For each w_(i)(

), the decoder removes the mask, p_(i)=(w_(i)+q_(i)) mod 2. Step 3: Foreach p_(i)(

), the decoder checks if the info bits associated with p_(i)(

) results in a successful parity check.

Step 4: If no parity check for each p_(i)(

) are successful, the decoding process can terminate and deliver the‘decoding failure’ message as the decoder output. If parity check(s) forone or more of p_(i)(

) are successful, then the decoding process continues normally.

FIG. 7 is a flow diagram illustrating an example method in a wirelesstransmitter, according to particular embodiments. In particularembodiments, one or more steps of FIG. 7 may be performed by networknode 120 or wireless device 110 of network 100 described with respect toFIG. 2.

The method begins at step 712, where a wireless transmitter encodes aset of information carrying data bits u of length K with a linear outercode to generate a set of outer parity bits p along with the data bitsu. For example, network node 120 may encode a set of outer parity bits(e.g., using a CRC) and data bits according to any of the embodimentsand examples described above with respect to FIGS. 3-6.

At step 714, the wireless transmitter interleaves the set of outerparity bits p and the data bits u using a predetermined interleavingmapping function that depends on the number of data bits K and isoperable to distribute some bits of the set of parity bits p in front ofsome data bits u. For example, network node 120 may interleave the setof outer parity bits p and the data bits u using any of the embodimentsand examples described above with respect to FIGS. 3-6.

At step 716, the wireless transmitter encodes the interleaved bits usinga polar encoder to generate a set of encoded bits x. For example,network node 120 may encode the interleaved bits according to any of theembodiments and examples described above with respect to FIGS. 3-6.

At step 718, the wireless transmitter may transmit the set of encodedbits x to a wireless receiver. For example, network node 120 transmitsthe set of encoded bits x to wireless device 110.

Modifications, additions, or omissions may be made to method 700 of FIG.7. Additionally, one or more steps in the method of FIG. 7 may beperformed in parallel or in any suitable order. The steps may berepeated over time as necessary.

FIG. 8 is a flow diagram illustrating an example method in a wirelessreceiver, according to particular embodiments. In particularembodiments, one or more steps of FIG. 8 may be performed by networknode 120 or wireless device 110 of network 100 described with respect toFIG. 2.

The method begins at step 812, where a wireless receiver determines thata decoder reaches a distributed CRC bit p_(i) when decoding a receivedset of polar encoded bits. For example, wireless device 110 may decode aset of polar encoded bits according to any of the deinterleavingembodiments or examples described above, such as successive cancellationlist (SCL) decoding.

At step 814, the wireless receiver calculates L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1. For example, wireless device 110 may estimate a listof values for a parity bit.

At step 814, for each p_(i)(

), the wireless receiver determines whether the info bits associatedwith p_(i)(

) leads to a successful parity check. For example, wireless device 110determines if a data bit was correctly received using the list of valuesfor the parity bit. If the decoding is not successful, then the methodcontinues to step 816 where the wireless receiver terminates thedecoding. If the decoding is successful, then the method continues tostep 818 where the wireless receiver continues the decoding.

Modifications, additions, or omissions may be made to method 800 of FIG.8. Additionally, one or more steps in the method of FIG. 8 may beperformed in parallel or in any suitable order. The steps may berepeated over time as necessary.

FIG. 9A is a block diagram illustrating an example embodiment of awireless device. The wireless device is an example of the wirelessdevices 110 illustrated in FIG. 2. In particular embodiments, thewireless device is capable of encoding and decoding a transmission usinga CRC interleaving pattern for polar codes.

Particular examples of a wireless device include a mobile phone, a smartphone, a PDA (Personal Digital Assistant), a portable computer (e.g.,laptop, tablet), a sensor, a modem, a machine type (MTC) device/machineto machine (M2M) device, laptop embedded equipment (LEE), laptop mountedequipment (LME), USB dongles, a device-to-device capable device, avehicle-to-vehicle device, or any other device that can provide wirelesscommunication. The wireless device includes transceiver 1310, processingcircuitry 1320, memory 1330, and power source 1340. In some embodiments,transceiver 1310 facilitates transmitting wireless signals to andreceiving wireless signals from wireless network node 120 (e.g., via anantenna), processing circuitry 1320 executes instructions to providesome or all of the functionality described herein as provided by thewireless device, and memory 1330 stores the instructions executed byprocessing circuitry 1320. Power source 1340 supplies electrical powerto one or more of the components of wireless device 110, such astransceiver 1310, processing circuitry 1320, and/or memory 1330.

Processing circuitry 1320 includes any suitable combination of hardwareand software implemented in one or more integrated circuits or modulesto execute instructions and manipulate data to perform some or all ofthe described functions of the wireless device. In some embodiments,processing circuitry 1320 may include, for example, one or morecomputers, one more programmable logic devices, one or more centralprocessing units (CPUs), one or more microprocessors, one or moreapplications, and/or other logic, and/or any suitable combination of thepreceding. Processing circuitry 1320 may include analog and/or digitalcircuitry configured to perform some or all of the described functionsof wireless device 110. For example, processing circuitry 1320 mayinclude resistors, capacitors, inductors, transistors, diodes, and/orany other suitable circuit components.

Memory 1330 is generally operable to store computer executable code anddata. Examples of memory 1330 include computer memory (e.g., RandomAccess Memory (RAM) or Read Only Memory (ROM)), mass storage media(e.g., a hard disk), removable storage media (e.g., a Compact Disk (CD)or a Digital Video Disk (DVD)), and/or or any other volatile ornon-volatile, non-transitory computer-readable and/orcomputer-executable memory devices that store information.

Power source 1340 is generally operable to supply electrical power tothe components of wireless device 110. Power source 1340 may include anysuitable type of battery, such as lithium-ion, lithium-air, lithiumpolymer, nickel cadmium, nickel metal hydride, or any other suitabletype of battery for supplying power to a wireless device.

Other embodiments of the wireless device may include additionalcomponents (beyond those shown in FIG. 9A) responsible for providingcertain aspects of the wireless device's functionality, including any ofthe functionality described above and/or any additional functionality(including any functionality necessary to support the solution describedabove).

FIG. 9B is a block diagram illustrating example components of a wirelessdevice 110. The components may include encoding/decoding module 1350,transmitting module 1352 and receiving module 1354.

Encoding/decoding module 1350 may perform the encoding and decodingfunctions of wireless device 110. For example, encoding/decoding module1350 may encode and decode a set of bits according to any of the CRCinterleaving examples and embodiments described above. In someembodiments, encoding/decoding module 1350 may perform only encoding,may perform only decoding, or may perform both encoding and decoding. Incertain embodiments, encoding/decoding module 1350 may include or beincluded in processing circuitry 1320. In particular embodiments,encoding/decoding module 1350 may communicate with transmitting module1352 and receiving module 1354.

Transmitting module 1352 may perform the transmitting functions ofwireless device 110. For example, transmitting module 1352 may transmitan encoded set of bits to network node 120. In certain embodiments,transmitting module 1352 may include or be included in processingcircuitry 1320. In particular embodiments, transmitting module 1352 maycommunicate with scheduling module 1350 and receiving module 1354.

Receiving module 1354 may perform the receiving functions of wirelessdevice 110. For example, receiving module 1354 may receive an encodedset of bits from network node 120. In certain embodiments, receivingmodule 1354 may include or be included in processing circuitry 1320. Inparticular embodiments, transmitting module 1352 may communicate withscheduling module 1350 and transmitting module 1352.

FIG. 10A is a block diagram illustrating an example embodiment of anetwork node. The network node is an example of the network node 120illustrated in FIG. 2. In particular embodiments, the network node iscapable of encoding and decoding a transmission using a CRC interleavingpattern for polar codes.

Network node 120 can be an eNodeB, a nodeB, gNB, a base station, awireless access point (e.g., a Wi-Fi access point), a low power node, abase transceiver station (BTS), a transmission point or node, a remoteRF unit (RRU), a remote radio head (RRH), or other radio access node.The network node includes at least one transceiver 1410, at least oneprocessing circuitry 1420, at least one memory 1430, and at least onenetwork interface 1440. Transceiver 1410 facilitates transmittingwireless signals to and receiving wireless signals from a wirelessdevice, such as wireless devices 110 (e.g., via an antenna); processingcircuitry 1420 executes instructions to provide some or all of thefunctionality described above as being provided by a network node 120;memory 1430 stores the instructions executed by processing circuitry1420; and network interface 1440 communicates signals to backend networkcomponents, such as a gateway, switch, router, Internet, Public SwitchedTelephone Network (PSTN), controller, and/or other network nodes 120.Processing circuitry 1420 and memory 1430 can be of the same types asdescribed with respect to processing circuitry 1320 and memory 1330 ofFIG. 9A above.

In some embodiments, network interface 1440 is communicatively coupledto processing circuitry 1420 and refers to any suitable device operableto receive input for network node 120, send output from network node120, perform suitable processing of the input or output or both,communicate to other devices, or any combination of the preceding.Network interface 1440 includes appropriate hardware (e.g., port, modem,network interface card, etc.) and software, including protocolconversion and data processing capabilities, to communicate through anetwork.

FIG. 10B is a block diagram illustrating example components of a networknode 120. The components may include encoding/decoding module 1450,transmitting module 1452 and receiving module 1454.

Encoding/decoding module 1450 may perform the encoding and decodingfunctions of network node 120. For example, encoding/decoding module1450 may encode and decode a set of bits according to any of the CRCinterleaving examples and embodiments described above. In someembodiments, encoding/decoding module 1450 may perform only encoding,may perform only decoding, or may perform both encoding and decoding. Incertain embodiments, encoding/decoding module 1450 may include or beincluded in processing circuitry 1420. In particular embodiments,encoding/decoding module 1450 may communicate with transmitting module1452 and receiving module 1454.

Transmitting module 1452 may perform the transmitting functions ofnetwork node 120. For example, transmitting module 1452 may transmit anencoded set of bits to wireless device 110. In certain embodiments,transmitting module 1452 may include or be included in processingcircuitry 1420. In particular embodiments, transmitting module 1452 maycommunicate with encoding/decoding module 1450 and receiving module1454.

Receiving module 1454 may perform the receiving functions of networknode 120. For example, receiving module 1454 may receive an encoded setof bits from wireless device 110. In certain embodiments, receivingmodule 1454 may include or be included in processing circuitry 1420. Inparticular embodiments, transmitting module 1452 may communicate withencoding/decoding module 1450 and transmitting module 1452.

Modifications, additions, or omissions may be made to the systems andapparatuses disclosed herein without departing from the scope of theinvention. The components of the systems and apparatuses may beintegrated or separated. Moreover, the operations of the systems andapparatuses may be performed by more, fewer, or other components.Additionally, operations of the systems and apparatuses may be performedusing any suitable logic comprising software, hardware, and/or otherlogic. As used in this document, “each” refers to each member of a setor each member of a subset of a set.

Modifications, additions, or omissions may be made to the methodsdisclosed herein without departing from the scope of the invention. Themethods may include more, fewer, or other steps. Additionally, steps maybe performed in any suitable order.

Although this disclosure has been described in terms of certainembodiments, alterations and permutations of the embodiments will beapparent to those skilled in the art. Accordingly, the above descriptionof the embodiments does not constrain this disclosure. Other changes,substitutions, and alterations are possible without departing from thespirit and scope of this disclosure, as defined by the claims below.

Abbreviations used in the preceding description include:

3GPP Third Generation Partnership Project

BBU Baseband Unit

BTS Base Transceiver Station

CC Component Carrier

CRC Cyclic Redundancy Check

CQI Channel Quality Information

CSI Channel State Information

D2D Device to Device

DCI Downlink Control Information

DFT Discrete Fourier Transform

DMRS Demodulation Reference Signal

eNB eNodeB

FDD Frequency Division Duplex

FFT Fast Fourier Transform

gNB Next-generation NodeB

LAA Licensed-Assisted Access

LBT Listen-before-talk

LDPC Low-Density Parity Check

LTE Long Term Evolution

LTE-U LTE in Unlicensed Spectrum

M2M Machine to Machine

MCS Modulation and Coding Scheme

MIB Master Information Block

MIMO Multi-Input Multi-Output

MTC Machine Type Communication

NR New Radio

OFDM Orthogonal Frequency Division Multiplexing

PCM Parity Check Matrix

PRB Physical Resource Block

RAN Radio Access Network

RAT Radio Access Technology

RBS Radio Base Station

RNC Radio Network Controller

RRC Radio Resource Control

RRH Remote Radio Head

RRU Remote Radio Unit

SCell Secondary Cell

SI System Information

SIB System Information Block

TB Transport Block

TBS Transport Block Size

TDD Time Division Duplex

TTI Transmission Time Interval

UE User Equipment

UL Uplink

UTRAN Universal Terrestrial Radio Access Network

WAN Wireless Access Network

1. A method of operation of a wireless transmitter in a wirelesscommunication network, the method comprising: encoding a set ofinformation carrying data bits u of length K with a linear outer code togenerate a set of outer parity bits p along with the data bits u;interleaving the set of outer parity bits p and the data bits u using apredetermined interleaving mapping function that depends on the numberof data bits K and is operable to distribute some bits of the set ofparity bits p in front of some data bits u; and encoding the interleavedbits using a polar encoder to generate a set of encoded bits x.
 2. Themethod of claim 1, further comprising transmitting the set of encodedbits x to a wireless receiver.
 3. The method of claim 1, wherein thepredetermined interleaving mapping function comprises a templateinterleaver for a largest value of K, referred to as K_(max), and thetemplate interleaver comprises a high-index bit mapper wherein: the Kdata bits are loaded at the high-index positions of the input of thetemplate interleaver, where u=[u₀, u₁, . . . , u_(K-1)] and the input ofthe template interleaver, denoted by v=[v₀, v₁, . . . , v_(K) _(max)₋₁], is given by the following bit mapping:$v_{i} = \left\{ {\begin{matrix}u_{i - K_{\max} + K} & {{K_{\max} - K} \leq i < K_{\max}} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {otherwise}\end{matrix}.} \right.$
 4. The method of claim 1, wherein thepredetermined interleaving mapping function comprises a templateinterleaver for a largest value of K, referred to as K_(max), and thetemplate interleaver comprises a low-index bit mapper wherein: the Kdata bits are loaded at the low-index positions of the input of thetemplate interleaver in reverse, where u=[u₀, u₁, . . . , u_(K-1)] andthe input of the template interleaver, denoted by v=[v₀, v₁, . . . ,v_(K) _(max) ₋₁], is given by the following bit mapping:${v_{i} = \left\{ \begin{matrix}u_{K - 1 - i} & {0 \leq i < K} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {{othe}r{wise}}\end{matrix} \right.}.$
 5. The method of claim 3, wherein K_(max) is 53and the template interleaver uses an interleaving pattern comprising anyone of the following interleaving patterns, wherein indicescorresponding to cyclic redundancy check (CRC) bits are underlined: (a)ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46 48 51 52 5812 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41 50 61 0 34 36 43 5340 49 54 29 42 64 13 65 2 62 23 55 69 71 3 56 57 67 6 59 60 63 66 70];(b) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46 48 51 5258 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41 50 61 0 2 3 6 1323 29 34 36 40 42 43 49 53 54 55 56 57 59 60 62 63 64 65 66 67 69 7071]; (c) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 46 4851 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41 50 61 0 3436 43 53 2 3 6 13 23 29 40 42 49 54 55 56 57 59 60 62 63 64 65 66 67 6970 71]; (d) ϕ_(T)=[1 4 5 8 10 11 14 15 16 20 24 26 28 30 31 35 44 45 4648 51 52 58 12 19 21 22 25 32 33 37 38 39 47 68 7 9 17 18 27 41 50 61 034 36 43 53 40 49 54 2 3 6 13 23 29 42 55 56 57 59 60 62 63 64 65 66 6769 70 71].
 6. The method of claim 4, wherein K_(max) is 53 and thetemplate interleaver uses an interleaving pattern comprising any one ofthe following interleaving patterns, wherein indices corresponding tocyclic redundancy check (CRC) bits are underlined: (a) ϕ_(T)=[0 1 4 6 78 17 21 22 24 26 28 32 36 37 38 41 42 44 47 48 51 58 5 13 14 15 19 20 2730 31 33 40 68 2 11 25 34 35 43 45 61 9 16 18 52 53 3 12 54 10 23 64 3965 50 62 29 55 69 71 49 56 57 67 46 59 60 63 66 70]; (b) ϕ_(T)=[51 48 4744 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6 4 1 0 58 40 33 31 30 27 2019 15 14 13 5 68 45 43 35 34 25 11 2 61 52 18 16 9 53 12 3 54 23 10 6439 65 50 62 29 55 69 71 49 56 67 57 46 59 66 60 70 63]; (c) ϕ_(T)=[0 1 46 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47 48 51 58 5 13 14 15 1920 27 30 31 33 40 68 2 11 25 34 35 43 45 61 3 9 10 12 16 18 23 29 39 4649 50 52 53 54 55 56 57 59 60 62 63 64 65 66 67 69 70 71]; (d) ϕ_(T)=[5148 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6 4 1 0 58 40 33 31 3027 20 19 15 14 13 5 68 45 43 35 34 25 11 2 61 3 9 10 12 16 18 23 29 3946 49 50 52 53 54 55 56 57 59 60 62 63 64 65 66 67 69 70 71]; (e)ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47 48 51 58 513 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45 61 9 16 18 52 53 310 12 23 29 39 46 49 50 54 55 56 57 59 60 62 63 64 65 66 67 69 70 71];(f) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 6 4 1 058 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2 61 52 18 16 953 3 10 12 23 29 39 46 49 50 54 55 56 57 59 60 62 63 64 65 66 67 69 7071]; (g) ϕ_(T)=[0 1 4 6 7 8 17 21 22 24 26 28 32 36 37 38 41 42 44 47 4851 58 5 13 14 15 19 20 27 30 31 33 40 68 2 11 25 34 35 43 45 61 9 16 1852 53 3 12 54 10 23 29 39 46 49 50 55 56 57 59 60 62 63 64 65 66 67 6970 71]; (h) ϕ_(T)=[51 48 47 44 42 41 38 37 36 32 28 26 24 22 21 17 8 7 64 1 0 58 40 33 31 30 27 20 19 15 14 13 5 68 45 43 35 34 25 11 2 61 52 1816 9 53 12 3 54 10 23 29 39 46 49 50 55 56 57 59 60 62 63 64 65 66 67 6970 71].
 7. The method of claim 3, wherein K_(max) is 72 and the templateinterleaver uses an interleaving pattern comprising any one of thefollowing interleaving patterns, wherein indices corresponding to cyclicredundancy check (CRC) bits are underlined: (a) ϕ_(T)=[3 4 8 11 13 14 1718 23 30 31 34 38 40 41 43 44 45 47 49 51 52 56 57 58 63 64 65 66 71 875 7 9 12 16 20 24 27 29 33 35 39 50 54 67 70 77 0 15 26 28 36 37 46 6069 80 1 19 55 59 68 73 32 53 61 84 10 62 72 21 81 48 83 22 76 42 88 2 7475 25 82 85 6 78 79 86 89 90]; (b) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 3134 38 40 41 43 44 45 47 49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 1620 24 27 29 33 35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 2 610 19 21 22 25 32 42 48 53 55 59 61 62 68 72 73 74 75 76 78 79 81 82 8384 85 86 88 89 90]; (c) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 4143 44 45 47 49 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 2933 35 39 50 54 67 70 77 0 15 26 28 36 37 46 60 69 80 1 19 55 59 68 73 26 10 21 22 25 32 42 48 53 61 62 72 74 75 76 78 79 81 82 83 84 85 86 8889 90]; (d) ϕ_(T)=[3 4 8 11 13 14 17 18 23 30 31 34 38 40 41 43 44 45 4749 51 52 56 57 58 63 64 65 66 71 87 5 7 9 12 16 20 24 27 29 33 35 39 5054 67 70 77 0 15 26 28 36 37 46 60 69 80 1 19 55 59 68 73 32 53 61 84 26 10 21 22 25 42 48 62 72 74 75 76 78 79 81 82 83 85 86 88 89 90]. 8.The method of claim 4, wherein K_(max) is 72 and the templateinterleaver uses an interleaving pattern comprising any one of thefollowing interleaving patterns, wherein indices corresponding to cyclicredundancy check (CRC) bits are underlined: (a) ϕ_(T)=[0 5 6 7 8 13 1415 19 20 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 58 60 63 67 68 871 4 17 21 32 36 38 42 44 47 51 55 59 62 64 66 77 2 11 25 34 35 43 45 5671 80 3 12 16 52 70 73 10 18 39 84 9 61 72 50 81 23 83 49 76 29 88 69 7475 46 82 85 65 78 79 86 89 90]; (b) ϕ_(T)=[68 67 63 60 58 57 54 53 48 4140 37 33 31 30 28 27 26 24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 5551 47 44 42 38 36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 70 52 1612 3 73 39 18 10 84 61 9 72 50 81 23 83 49 76 29 88 69 74 75 46 82 85 6586 79 78 89 90]; (c) ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 3031 33 37 40 41 48 53 54 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 4751 55 59 62 64 66 77 2 11 25 34 35 43 45 56 71 80 3 9 10 12 16 18 23 2939 46 49 50 52 61 65 69 70 72 73 74 75 76 78 79 81 82 83 84 85 86 88 8990]; (d) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 2422 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 51 47 44 42 38 36 32 21 174 1 77 71 56 45 43 35 34 25 11 2 80 3 9 10 12 16 18 23 29 39 46 49 50 5261 65 69 70 72 73 74 75 76 78 79 81 82 83 84 85 86 88 89 90]; (e)ϕ_(T)=[0 5 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37 40 41 48 5354 57 58 60 63 67 68 87 1 4 17 21 32 36 38 42 44 47 51 55 59 62 64 66 772 11 25 34 35 43 45 56 71 80 3 12 16 52 70 73 9 10 18 23 29 39 46 49 5061 65 69 72 74 75 76 78 79 81 82 83 84 85 86 88 89 90]; (f) ϕ_(T)=[68 6763 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22 20 19 15 14 13 8 76 5 0 87 66 64 62 59 55 51 47 44 42 38 36 32 21 17 4 1 77 71 56 45 43 3534 25 11 2 80 70 52 16 12 3 73 9 10 18 23 29 39 46 49 50 61 65 69 72 7475 76 78 79 81 82 83 84 85 86 88 89 90]; (g) ϕ_(T)=[0 5 6 7 8 13 14 1519 20 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 58 60 63 67 68 87 1 417 21 32 36 38 42 44 47 51 55 59 62 64 66 77 2 11 25 34 35 43 45 56 7180 3 12 16 52 70 73 10 18 39 84 9 23 29 46 49 50 61 65 69 72 74 75 76 7879 81 82 83 85 86 88 89 90]; (h) ϕ_(T)=[68 67 63 60 58 57 54 53 48 41 4037 33 31 30 28 27 26 24 22 20 19 15 14 13 8 7 6 5 0 87 66 64 62 59 55 5147 44 42 38 36 32 21 17 4 1 77 71 56 45 43 35 34 25 11 2 80 70 52 16 123 73 39 18 10 84 9 23 29 46 49 50 61 65 69 72 74 75 76 78 79 81 82 83 8586 88 89 90].
 9. The method of claim 3, wherein K_(max) is 140 and thetemplate interleaver uses an interleaving pattern comprising any one ofthe following interleaving patterns, wherein indices corresponding tocyclic redundancy check (CRC) bits are underlined: (a) ϕ_(T)=[0 3 6 9 1112 13 14 15 17 18 19 21 22 28 29 30 37 38 42 43 48 53 57 59 64 65 66 6971 72 73 78 79 91 92 97 106 111 114 117 119 122 125 126 127 128 130 131134 136 137 144 1 4 7 10 16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98107 112 115 118 120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 6168 75 81 94 99 108 113 116 121 124 133 139 146 26 33 34 41 46 77 83 8788 89 100 101 104 109 110 147 25 51 56 62 76 82 95 140 27 84 86 96 102161 36 103 105 150 90 159 52 163 63 153 47 143 85 151 158 160 162 35 141142 148 149 152 154 155 156 157]; (b) ϕ_(T)=[0 3 6 9 11 12 13 14 15 1718 19 21 22 28 29 30 37 38 42 43 48 53 57 59 64 65 66 69 71 72 73 78 7991 92 97 106 111 114 117 119 122 125 126 127 128 130 131 134 136 137 1441 4 7 10 16 20 23 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118120 123 129 132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81 94 99108 113 116 121 124 133 139 146 25 26 27 33 34 35 36 41 46 47 51 52 5662 63 76 77 82 83 84 85 86 87 88 89 90 95 96 100 101 102 103 104 105 109110 140 141 142 143 147 148 149 150 151 152 153 154 155 156 157 158 159160 161 162 163]; (c) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 2930 37 38 42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111114 117 119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10 16 2023 31 39 44 49 54 58 60 67 70 74 80 93 98 107 112 115 118 120 123 129132 135 138 145 2 5 8 24 32 40 45 50 55 61 68 75 81 94 99 108 113 116121 124 133 139 146 26 33 34 41 46 77 83 87 88 89 100 101 104 109 110147 25 27 35 36 47 51 52 56 62 63 76 82 84 85 86 90 95 96 102 103 105140 141 142 143 148 149 150 151 152 153 154 155 156 157 158 159 160 161162 163]; (d) ϕ_(T)=[0 3 6 9 11 12 13 14 15 17 18 19 21 22 28 29 30 3738 42 43 48 53 57 59 64 65 66 69 71 72 73 78 79 91 92 97 106 111 114 117119 122 125 126 127 128 130 131 134 136 137 144 1 4 7 10 16 20 23 31 3944 49 54 58 60 67 70 74 80 93 98 107 112 115 118 120 123 129 132 135 138145 2 5 8 24 32 40 45 50 55 61 68 75 81 94 99 108 113 116 121 124 133139 146 26 33 34 41 46 77 83 87 88 89 100 101 104 109 110 147 25 51 5662 76 82 95 140 27 35 36 47 52 63 84 85 86 90 96 102 103 105 141 142 143148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (e)ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51 53 54 56 5859 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88 89 91 93 95 98 101104 106 108 110 111 113 115 118 119 120 122 123 126 127 129 132 134 138139 140 1 3 5 8 10 15 21 27 29 32 35 43 46 52 55 57 60 63 68 73 78 84 9092 94 96 99 102 105 107 109 112 114 116 121 124 128 130 133 135 141 6 1116 22 30 33 36 44 47 64 74 79 85 97 100 103 117 125 131 136 142 12 17 2337 48 75 80 86 137 143 13 18 38 144 39 145 40 146 41 147 148 149 150 151152 153 154 155 156 157 158 159 160 161 162 163]; (f) ϕ_(T)=[0 2 4 7 914 19 20 24 25 26 28 31 34 42 45 49 50 51 53 54 56 58 59 61 62 65 66 6769 70 71 72 76 77 81 82 83 87 88 89 91 93 95 98 101 104 106 108 110 111113 115 118 119 120 122 123 126 127 129 132 134 138 139 140 1 3 5 8 1015 21 27 29 32 35 43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102105 107 109 112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 3644 47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 17 18 23 37 38 3940 41 48 75 80 86 137 143 144 145 146 147 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (g) ϕ_(T)=[0 2 4 7 9 14 19 20 2425 26 28 31 34 42 45 49 50 51 53 54 56 58 59 61 62 65 66 67 69 70 71 7276 77 81 82 83 87 88 89 91 93 95 98 101 104 106 108 110 111 113 115 118119 120 122 123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 2932 35 43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44 47 64 7479 85 97 100 103 117 125 131 136 142 12 17 23 37 48 75 80 86 137 143 1318 38 39 40 41 144 145 146 147 148 149 150 151 152 153 154 155 156 157158 159 160 161 162 163]; (h) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 3134 42 45 49 50 51 53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 8283 87 88 89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35 43 4652 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109 112 114 116121 124 128 130 133 135 141 6 11 16 22 30 33 36 44 47 64 74 79 85 97 100103 117 125 131 136 142 12 17 23 37 48 75 80 86 137 143 13 18 38 144 3940 41 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160161 162 163]; (i) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 4950 51 53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88 8991 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122 123 126 127129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35 43 46 52 55 57 6063 68 73 78 84 90 92 94 96 99 102 105 107 109 112 114 116 121 124 128130 133 135 141 6 11 16 22 30 33 36 44 47 64 74 79 85 97 100 103 117 125131 136 142 12 17 23 37 48 75 80 86 137 143 13 18 38 144 39 145 40 41146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162163]; (j) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51 5354 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88 89 91 93 9598 101 104 106 108 110 111 113 115 118 119 120 122 123 126 127 129 132134 138 139 140 1 3 5 8 10 15 21 27 29 32 35 43 46 52 55 57 60 63 68 7378 84 90 92 94 96 99 102 105 107 109 112 114 116 121 124 128 130 133 135141 6 11 16 22 30 33 36 44 47 64 74 79 85 97 100 103 117 125 131 136 14212 13 18 23 38 39 80 137 145 17 40 75 146 48 149 37 86 143 144 41 147148 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (k)ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 31 34 42 45 49 50 51 53 54 56 5859 61 62 65 66 67 69 70 71 72 76 77 81 82 83 87 88 89 91 93 95 98 101104 106 108 110 111 113 115 118 119 120 122 123 126 127 129 132 134 138139 140 1 3 5 8 10 15 21 27 29 32 35 43 46 52 55 57 60 63 68 73 78 84 9092 94 96 99 102 105 107 109 112 114 116 121 124 128 130 133 135 141 6 1116 22 30 33 36 44 47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 1718 23 37 38 39 40 41 48 75 80 86 137 143 144 145 146 147 148 149 150 151152 153 154 155 156 157 158 159 160 161 162 163]; (l) ϕ_(PT)=[0 2 4 7 914 19 20 24 25 26 28 31 34 42 45 49 50 51 53 54 56 58 59 61 62 65 66 6769 70 71 72 76 77 81 82 83 87 88 89 91 93 95 98 101 104 106 108 110 111113 115 118 119 120 122 123 126 127 129 132 134 138 139 140 1 3 5 8 1015 21 27 29 32 35 43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102105 107 109 112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 3644 47 64 74 79 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39 80137 145 17 37 40 41 48 75 86 143 144 146 147 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (m) ϕ_(T)=[0 2 4 7 9 14 19 20 2425 26 28 31 34 42 45 49 50 51 53 54 56 58 59 61 62 65 66 67 69 70 71 7276 77 81 82 83 87 88 89 91 93 95 98 101 104 106 108 110 111 113 115 118119 120 122 123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 2932 35 43 46 52 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109112 114 116 121 124 128 130 133 135 141 6 11 16 22 30 33 36 44 47 64 7479 85 97 100 103 117 125 131 136 142 12 13 18 23 38 39 80 137 145 17 4075 146 37 41 48 86 143 144 147 148 149 150 151 152 153 154 155 156 157158 159 160 161 162 163]; (n) ϕ_(T)=[0 2 4 7 9 14 19 20 24 25 26 28 3134 42 45 49 50 51 53 54 56 58 59 61 62 65 66 67 69 70 71 72 76 77 81 8283 87 88 89 91 93 95 98 101 104 106 108 110 111 113 115 118 119 120 122123 126 127 129 132 134 138 139 140 1 3 5 8 10 15 21 27 29 32 35 43 4652 55 57 60 63 68 73 78 84 90 92 94 96 99 102 105 107 109 112 114 116121 124 128 130 133 135 141 6 11 16 22 30 33 36 44 47 64 74 79 85 97 100103 117 125 131 136 142 12 13 18 23 38 39 80 137 145 17 40 75 146 48 14937 41 86 143 144 147 148 150 151 152 153 154 155 156 157 158 159 160 161162 163]; (o) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 3839 41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85 86 9198 99 102 106 108 109 111 112 113 115 117 119 120 124 125 126 131 132133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57 60 61 63 64 77 84 8790 96 103 104 107 114 116 118 122 129 130 136 137 138 144 8 27 31 34 4950 65 74 93 94 95 97 100 101 105 121 127 147 13 26 36 54 73 75 89 92 135146 14 32 80 88 145 68 69 128 152 1 6 20 78 151 22 83 148 149 123 141 45140 70 153 154 110 142 143 150 156 157 158]; (p) ϕ_(T)=[0 2 4 5 10 11 1216 18 19 23 24 25 28 33 35 37 38 39 41 42 47 48 51 52 53 55 56 58 59 6266 67 71 72 76 79 81 82 85 86 91 98 99 102 106 108 109 111 112 113 115117 119 120 124 125 126 131 132 133 134 139 155 3 7 9 15 17 21 29 30 4043 44 46 57 60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122 129130 136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105 121127 147 1 6 13 14 20 22 26 32 36 45 54 68 69 70 73 75 78 80 83 88 89 92110 123 128 135 140 141 142 143 145 146 148 149 150 151 152 153 154 156157 158]; (q) ϕ_(T)=[0 2 4 5 10 11 12 16 18 19 23 24 25 28 33 35 37 3839 41 42 47 48 51 52 53 55 56 58 59 62 66 67 71 72 76 79 81 82 85 86 9198 99 102 106 108 109 111 112 113 115 117 119 120 124 125 126 131 132133 134 139 155 3 7 9 15 17 21 29 30 40 43 44 46 57 60 61 63 64 77 84 8790 96 103 104 107 114 116 118 122 129 130 136 137 138 144 8 27 31 34 4950 65 74 93 94 95 97 100 101 105 121 127 147 13 26 36 54 73 75 89 92 135146 1 6 14 20 22 32 45 68 69 70 78 80 83 88 110 123 128 140 141 142 143145 148 149 150 151 152 153 154 156 157 158]; (r) ϕ_(T)=[0 2 4 5 10 1112 16 18 19 23 24 25 28 33 35 37 38 39 41 42 47 48 51 52 53 55 56 58 5962 66 67 71 72 76 79 81 82 85 86 91 98 99 102 106 108 109 111 112 113115 117 119 120 124 125 126 131 132 133 134 139 155 3 7 9 15 17 21 29 3040 43 44 46 57 60 61 63 64 77 84 87 90 96 103 104 107 114 116 118 122129 130 136 137 138 144 8 27 31 34 49 50 65 74 93 94 95 97 100 101 105121 127 147 13 26 36 54 73 75 89 92 135 146 14 32 80 88 145 1 6 20 22 4568 69 70 78 83 110 123 128 140 141 142 143 148 149 150 151 152 153 154156 157 158].
 10. The method of claim 4, wherein K_(max) is 140 and thetemplate interleaver uses an interleaving pattern comprising any one ofthe following interleaving patterns, wherein indices corresponding tocyclic redundancy check (CRC) bits are underlined: (a) ϕ_(T)=[2 3 5 8 911 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 80 8286 91 96 97 101 102 109 110 111 117 118 120 121 122 124 125 126 127 128130 133 136 139 144 1 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 8185 90 95 100 108 116 119 123 129 132 135 138 145 0 6 15 18 23 26 31 4045 58 64 71 78 84 89 94 99 107 115 131 134 137 146 29 30 35 38 39 50 5152 56 62 93 98 105 106 113 147 44 57 63 77 83 88 114 140 37 43 53 55 112161 34 36 103 150 49 159 87 163 76 153 92 143 54 151 158 160 162 104 141142 148 149 152 154 155 156 157]; (b) ϕ_(T)=[139 136 133 130 128 127 126125 124 122 121 120 118 117 111 110 109 102 101 97 96 91 86 82 80 75 7473 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2144 138 135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 4132 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84 78 71 6458 45 40 31 26 23 18 15 6 0 146 113 106 105 98 93 62 56 52 51 50 39 3835 30 29 147 114 88 83 77 63 57 44 140 112 55 53 43 37 161 103 36 34 15049 159 87 163 76 153 92 143 54 151 158 160 162 104 141 142 148 149 152154 155 156 157]; (c) [2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 4860 61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111 117 118120 121 122 124 125 126 127 128 130 133 136 139 144 1 4 7 10 16 19 21 2427 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135138 145 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99 107 115 131 134137 146 29 30 34 35 36 37 38 39 43 44 49 50 51 52 53 54 55 56 57 62 6376 77 83 87 88 92 93 98 103 104 105 106 112 113 114 140 141 142 143 147148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (d)ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118 117 111 110109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 2825 22 20 17 14 13 12 11 9 8 5 3 2 144 138 135 132 129 123 119 116 108100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1 145 137134 131 115 107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 146 114113 112 106 105 104 103 98 93 92 88 87 83 77 76 63 62 57 56 55 54 53 5251 50 49 44 43 39 38 37 36 35 34 30 29 140 141 142 143 147 148 149 150151 152 153 154 155 156 157 158 159 160 161 162 163]; (e) ϕ_(T)=[2 3 5 89 11 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 8082 86 91 96 97 101 102 109 110 111 117 118 120 121 122 124 125 126 127128 130 133 136 139 144 1 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 7981 85 90 95 100 108 116 119 123 129 132 135 138 145 0 6 15 18 23 26 3140 45 58 64 71 78 84 89 94 99 107 115 131 134 137 146 29 30 35 38 39 5051 52 56 62 93 98 105 106 113 147 34 36 37 43 44 49 53 54 55 57 63 76 7783 87 88 92 103 104 112 114 140 141 142 143 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (f) ϕ_(T)=[139 136 133 130 128 127126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91 86 82 80 7574 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2144 138 135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 4132 27 24 21 19 16 10 7 4 1 145 137 134 131 115 107 99 94 89 84 78 71 6458 45 40 31 26 23 18 15 6 0 146 113 106 105 98 93 62 56 52 51 50 39 3835 30 29 147 114 112 104 103 92 88 87 83 77 76 63 57 55 54 53 49 44 4337 36 34 140 141 142 143 148 149 150 151 152 153 154 155 156 157 158 159160 161 162 163]; (g) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 4247 48 60 61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111117 118 120 121 122 124 125 126 127 128 130 133 136 139 144 1 4 7 10 1619 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129132 135 138 145 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99 107 115131 134 137 146 29 30 35 38 39 50 51 52 56 62 93 98 105 106 113 147 4457 63 77 83 88 114 140 34 36 37 43 49 53 54 55 76 87 92 103 104 112 141142 143 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162163]; (h) ϕ_(T)=[139 136 133 130 128 127 126 125 124 122 121 120 118 117111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 4742 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 144 138 135 132 129 123 119116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1145 137 134 131 115 107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0146 113 106 105 98 93 62 56 52 51 50 39 38 35 30 29 147 114 88 83 77 6357 44 140 112 104 103 92 87 76 55 54 53 49 43 37 36 34 141 142 143 148149 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (i)ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 4648 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 8889 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137 139 1404 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 8284 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 3 8 14 22 3639 42 54 60 65 75 92 95 103 106 109 117 123 128 133 142 2 53 59 64 91102 116 122 127 143 101 121 126 144 100 145 99 146 98 147 148 149 150151 152 153 154 155 156 157 158 159 160 161 162 163]; (j) ϕ_(T)=[139 137135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 8381 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 3835 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 140 138 136 134 131129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 4340 37 34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 10395 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64 59 53 2143 126 121 101 144 100 145 99 146 98 147 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (k) ϕ_(T)=[0 1 5 7 10 12 13 16 1719 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 6768 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113114 115 119 120 125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 3032 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 142 2 53 59 64 91 98 99 100 101 102 116 121 122126 127 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158159 160 161 162 163]; (l) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 6763 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 1716 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112 110 107 104 9693 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 1511 9 6 4 141 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 2214 8 3 142 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 143 144145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162163]; (m) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 3841 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 8385 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137139 140 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 7176 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 3 814 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 142 2 53 5964 91 102 116 122 127 143 98 99 100 101 121 126 144 145 146 147 148 149150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (n) ϕ_(T)=[139137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 8583 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 4138 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 140 138 136 134131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 4745 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106103 95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 102 91 64 59 532 143 98 99 100 101 121 126 144 145 146 147 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (o) ϕ_(T)=[0 1 5 7 10 12 13 16 1719 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 6768 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113114 115 119 120 125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 3032 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 142 2 53 59 64 91 102 116 122 127 143 101 121126 144 98 99 100 145 146 147 148 149 150 151 152 153 154 155 156 157158 159 160 161 162 163]; (p) ϕ_(T)=[139 137 135 132 130 125 120 119 115114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 6968 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 2019 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118 112 110 107104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 2318 15 11 9 6 4 141 133 128 123 117 109 106 103 95 92 75 65 60 54 42 3936 22 14 8 3 142 127 122 116 102 91 64 59 53 2 143 126 121 101 144 98 99100 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161162 163]; (q) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 3335 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 8081 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130 132135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 6166 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136 138141 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 1422 53 59 64 91 102 116 122 127 143 101 121 126 144 100 145 98 99 146 147148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (r)ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 9089 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 5048 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 140138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 6661 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 142 127 122 116 10291 64 59 53 2 143 126 121 101 144 100 145 98 99 146 147 148 149 150 151152 153 154 155 156 157 158 159 160 161 162 163]; (s) ϕ_(T)=[0 1 5 7 1012 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 5758 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105108 111 113 114 115 119 120 125 130 132 135 137 139 140 4 6 9 11 15 1823 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104107 110 112 118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 60 6575 92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126 127145 64 99 122 146 91 149 53 102 143 144 98 147 148 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (t) ϕ_(T)=[139 137 135 132 130 125120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 7473 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 2826 24 21 20 19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 3230 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103 95 92 75 6560 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100 59 2 145 122 99 64146 91 149 102 53 143 144 98 147 148 150 151 152 153 154 155 156 157 158159 160 161 162 163]; (u) ϕ_(T)-[0 1 5 7 10 12 13 16 17 19 20 21 24 2628 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 7374 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 4547 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131134 136 138 141 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123128 133 142 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 143 144145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162163]; (v) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108 10597 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 5652 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 51 0 140 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 7671 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 141 133128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 142 2 53 5964 91 98 99 100 101 102 116 121 122 126 127 143 144 145 146 147 148 149150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (w) ϕ_(T)=[0 15 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 5256 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97105 108 111 113 114 115 119 120 125 130 132 135 137 139 140 4 6 9 11 1518 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96104 107 110 112 118 124 129 131 134 136 138 141 3 8 14 22 36 39 42 54 6065 75 92 95 103 106 109 117 123 128 133 142 2 59 100 101 116 121 126 127145 53 64 91 98 99 102 122 143 144 146 147 148 149 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (x) ϕ_(T)=[139 137 135 132 130 125120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 7473 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 2826 24 21 20 19 17 16 13 12 10 7 5 1 0 140 138 136 134 131 129 124 118112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 3230 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 103 95 92 75 6560 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100 59 2 145 53 64 9198 99 102 122 143 144 146 147 148 149 150 151 152 153 154 155 156 157158 159 160 161 162 163]; (y) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 2426 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 7273 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119120 125 130 132 135 137 139 140 4 6 9 11 15 18 23 25 27 30 32 34 37 4043 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129131 134 136 138 141 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117123 128 133 142 2 59 100 101 116 121 126 127 145 64 99 122 146 53 91 98102 143 144 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161162 163]; (z) ϕ_(T)=[139 137 135 132 130 125 120 119 115 114 113 111 108105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 5756 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 107 5 1 0 140 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 8279 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 141133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 142 127126 121 116 101 100 59 2 145 122 99 64 146 53 91 98 102 143 144 147 148149 150 151 152 153 154 155 156 157 158 159 160 161 162 163]; (aa)ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 4648 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 8889 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137 139 1404 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 8284 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 3 8 14 22 3639 42 54 60 65 75 92 95 103 106 109 117 123 128 133 142 2 59 100 101 116121 126 127 145 64 99 122 146 91 149 53 98 102 143 144 147 148 150 151152 153 154 155 156 157 158 159 160 161 162 163]; (bb) ϕ_(T)=[139 137135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 8381 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 3835 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 140 138 136 134 131129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 4340 37 34 32 30 27 25 23 18 15 11 9 6 4 141 133 128 123 117 109 106 10395 92 75 65 60 54 42 39 36 22 14 8 3 142 127 126 121 116 101 100 59 2145 122 99 64 146 91 149 53 98 102 143 144 147 148 150 151 152 153 154155 156 157 158 159 160 161 162 163]; (cc) ϕ_(T)=[0 5 6 7 8 13 14 15 1920 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 58 60 63 67 68 72 73 7780 81 83 84 86 87 88 91 92 97 98 100 101 102 104 106 111 114 115 116 120121 123 127 128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 25 32 35 3643 49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124 130 132136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112 131 147 4 4750 64 66 85 103 113 126 146 51 59 107 125 145 11 70 71 152 61 119 133138 151 56 117 148 149 16 141 94 140 69 153 154 29 142 143 150 156 157158]; (dd) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116 115 114111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 73 72 68 6763 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22 20 19 15 14 13 8 76 5 0 155 136 132 130 124 122 118 110 109 99 96 95 93 82 79 78 76 75 6255 52 49 43 36 35 32 25 23 21 17 10 9 3 2 1 144 131 112 108 105 90 89 7465 46 45 44 42 39 38 34 18 12 147 126 113 103 85 66 64 50 47 4 146 125107 59 51 145 71 70 11 152 138 133 119 61 151 117 56 148 149 16 141 94140 69 153 154 29 143 142 150 156 157 158]; (ee) ϕ_(T)=[0 5 6 7 8 13 1415 19 20 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 58 60 63 67 68 7273 77 80 81 83 84 86 87 88 91 92 97 98 100 101 102 104 106 111 114 115116 120 121 123 127 128 129 134 135 137 139 155 1 2 3 9 10 17 21 23 2532 35 36 43 49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122 124130 132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112 131147 4 11 16 29 47 50 51 56 59 61 64 66 69 70 71 85 94 103 107 113 117119 125 126 133 138 140 141 142 143 145 146 148 149 150 151 152 153 154156 157 158]; (ff) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120 116115 114 111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 77 7372 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22 20 19 1514 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99 96 95 93 82 79 7876 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9 3 2 1 144 131 112 108 10590 89 74 65 46 45 44 42 39 38 34 18 12 147 4 11 16 29 47 50 51 56 59 6164 66 69 70 71 85 94 103 107 113 117 119 125 126 133 138 140 141 142 143145 146 148 149 150 151 152 153 154 156 157 158]; (gg) ϕ_(T)-[0 5 6 7 813 14 15 19 20 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 58 60 63 6768 72 73 77 80 81 83 84 86 87 88 91 92 97 98 100 101 102 104 106 111 114115 116 120 121 123 127 128 129 134 135 137 139 155 1 2 3 9 10 17 21 2325 32 35 36 43 49 52 55 62 75 76 78 79 82 93 95 96 99 109 110 118 122124 130 132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90 105 108 112131 147 4 47 50 64 66 85 103 113 126 146 11 16 29 51 56 59 61 69 70 7194 107 117 119 125 133 138 140 141 142 143 145 148 149 150 151 152 153154 156 157 158]; (hh) ϕ_(T)=[139 137 135 134 129 128 127 123 121 120116 115 114 111 106 104 102 101 100 98 97 92 91 88 87 86 84 83 81 80 7773 72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 26 24 22 20 1915 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99 96 95 93 82 7978 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9 3 2 1 144 131 112 108105 90 89 74 65 46 45 44 42 39 38 34 18 12 147 126 113 103 85 66 64 5047 4 146 11 16 29 51 56 59 61 69 70 71 94 107 117 119 125 133 138 140141 142 143 145 148 149 150 151 152 153 154 156 157 158]; (ii) ϕ_(T)=[05 6 7 8 13 14 15 19 20 22 24 26 27 28 30 31 33 37 40 41 48 53 54 57 5860 63 67 68 72 73 77 80 81 83 84 86 87 88 91 92 97 98 100 101 102 104106 111 114 115 116 120 121 123 127 128 129 134 135 137 139 155 1 2 3 910 17 21 23 25 32 35 36 43 49 52 55 62 75 76 78 79 82 93 95 96 99 109110 118 122 124 130 132 136 144 12 18 34 38 39 42 44 45 46 65 74 89 90105 108 112 131 147 4 47 50 64 66 85 103 113 126 146 51 59 107 125 14511 16 29 56 61 69 70 71 94 117 119 133 138 140 141 142 143 148 149 150151 152 153 154 156 157 158]; (jj) ϕ_(T)=[139 137 135 134 129 128 127123 121 120 116 115 114 111 106 104 102 101 100 98 97 92 91 88 87 86 8483 81 80 77 73 72 68 67 63 60 58 57 54 53 48 41 40 37 33 31 30 28 27 2624 22 20 19 15 14 13 8 7 6 5 0 155 136 132 130 124 122 118 110 109 99 9695 93 82 79 78 76 75 62 55 52 49 43 36 35 32 25 23 21 17 10 9 3 2 1 144131 112 108 105 90 89 74 65 46 45 44 42 39 38 34 18 12 147 126 113 10385 66 64 50 47 4 146 125 107 59 51 145 11 16 29 56 61 69 70 71 94 117119 133 138 140 141 142 143 148 149 150 151 152 153 154 156 157 158].11. The method of claim 3, wherein K_(max) is 160 and the templateinterleaver uses an interleaving pattern comprising any one of thefollowing interleaving patterns, wherein indices corresponding to cyclicredundancy check (CRC) bits are underlined: (a) ϕ_(T)=[0 1 2 4 6 7 9 1014 15 17 19 20 22 24 27 29 34 39 40 44 45 46 48 51 54 62 65 69 70 71 7374 76 78 79 81 82 85 86 87 89 90 91 92 96 97 101 102 103 107 108 109 111113 115 118 121 124 126 128 130 131 133 135 138 139 140 142 143 146 147149 152 154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 5563 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125 127 129132 134 136 141 144 148 150 153 155 161 12 26 31 36 42 50 53 56 64 67 8494 99 105 117 120 123 137 145 151 156 162 13 32 37 43 57 68 95 100 106157 163 33 38 58 164 59 165 60 166 61 167 168 169 170 171 172 173 174175 176 177 178 179 180 181 182 183]; (b) ϕ_(T)=[0 3 4 5 7 12 16 18 2023 26 29 31 32 33 34 35 37 38 39 41 42 48 49 50 57 58 62 63 68 73 77 7984 85 86 89 91 92 93 98 99 111 112 117 126 131 134 137 139 142 145 146147 148 150 151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 5159 64 69 74 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152155 158 165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114 119 128133 136 141 144 153 159 166 46 53 54 61 66 97 103 107 108 109 120 121124 129 130 167 10 15 45 71 76 82 96 102 115 160 11 47 104 106 116 122181 56 123 125 170 110 179 72 183 83 173 67 163 105 171 178 180 182 55161 162 168 169 172 174 175 176 177]; (c) ϕ_(T)=[0 1 2 4 6 7 9 10 14 1517 19 20 22 24 27 29 34 39 40 44 45 46 48 51 54 62 65 69 70 71 73 74 7678 79 81 82 85 86 87 89 90 91 92 96 97 101 102 103 107 108 109 111 113115 118 121 124 126 128 130 131 133 135 138 139 140 142 143 146 147 149152 154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55 6366 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125 127 129 132134 136 141 144 148 150 153 155 161 12 26 31 36 42 50 53 56 64 67 84 9499 105 117 120 123 137 145 151 156 162 13 32 33 37 38 43 57 58 59 60 6168 95 100 106 157 163 164 165 166 167 168 169 170 171 172 173 174 175176 177 178 179 180 181 182 183]; (d) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 2629 31 32 33 34 35 37 38 39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 8586 89 91 92 93 98 99 111 112 117 126 131 134 137 139 142 145 146 147 148150 151 154 156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64 6974 78 80 87 90 94 100 113 118 127 132 135 138 140 143 149 152 155 158165 2 9 14 22 25 28 44 52 60 65 70 75 81 88 95 101 114 119 128 133 136141 144 153 159 166 10 11 15 45 46 47 53 54 55 56 61 66 67 71 72 76 8283 96 97 102 103 104 105 106 107 108 109 110 115 116 120 121 122 123 124125 129 130 160 161 162 163 167 168 169 170 171 172 173 174 175 176 177178 179 180 181 182 183]; (e) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 2224 27 29 34 39 40 44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 8285 86 87 89 90 91 92 96 97 101 102 103 107 108 109 111 113 115 118 121124 126 128 130 131 133 135 138 139 140 142 143 146 147 149 152 154 158159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55 63 66 72 75 7780 83 88 93 98 104 110 112 114 116 119 122 125 127 129 132 134 136 141144 148 150 153 155 161 12 26 31 36 42 50 53 56 64 67 84 94 99 105 117120 123 137 145 151 156 162 13 32 37 43 57 68 95 100 106 157 163 33 3858 59 60 61 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178179 180 181 182 183]; (f) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 3334 35 37 38 39 41 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 9293 98 99 111 112 117 126 131 134 137 139 142 145 146 147 148 150 151 154156 157 164 1 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64 69 74 78 80 8790 94 100 113 118 127 132 135 138 140 143 149 152 155 158 165 2 9 14 2225 28 44 52 60 65 70 75 81 88 95 101 114 119 128 133 136 141 144 153 159166 46 53 54 61 66 97 103 107 108 109 120 121 124 129 130 167 10 11 1545 47 55 56 67 71 72 76 82 83 96 102 104 105 106 110 115 116 122 123 125160 161 162 163 168 169 170 171 172 173 174 175 176 177 178 179 180 181182 183]; (g) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 3940 44 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87 89 9091 92 96 97 101 102 103 107 108 109 111 113 115 118 121 124 126 128 130131 133 135 138 139 140 142 143 146 147 149 152 154 158 159 160 3 5 8 1116 18 21 23 25 28 30 35 41 47 49 52 55 63 66 72 75 77 80 83 88 93 98 104110 112 114 116 119 122 125 127 129 132 134 136 141 144 148 150 153 155161 12 26 31 36 42 50 53 56 64 67 84 94 99 105 117 120 123 137 145 151156 162 13 32 37 43 57 68 95 100 106 157 163 33 38 58 164 59 60 61 165166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (h) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38 3941 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93 98 99 111112 117 126 131 134 137 139 142 145 146 147 148 150 151 154 156 157 1641 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64 69 74 78 80 87 90 94 100113 118 127 132 135 138 140 143 149 152 155 158 165 2 9 14 22 25 28 4452 60 65 70 75 81 88 95 101 114 119 128 133 136 141 144 153 159 166 4653 54 61 66 97 103 107 108 109 120 121 124 129 130 167 10 15 45 71 76 8296 102 115 160 11 47 55 56 67 72 83 104 105 106 110 116 122 123 125 161162 163 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (i) ϕ_(PT)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 4044 45 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87 89 90 9192 96 97 101 102 103 107 108 109 111 113 115 118 121 124 126 128 130 131133 135 138 139 140 142 143 146 147 149 152 154 158 159 160 3 5 8 11 1618 21 23 25 28 30 35 41 47 49 52 55 63 66 72 75 77 80 83 88 93 98 104110 112 114 116 119 122 125 127 129 132 134 136 141 144 148 150 153 155161 12 26 31 36 42 50 53 56 64 67 84 94 99 105 117 120 123 137 145 151156 162 13 32 37 43 57 68 95 100 106 157 163 33 38 58 164 59 165 60 61166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (j) ϕ_(T)=[0 3 4 5 7 12 16 18 20 23 26 29 31 32 33 34 35 37 38 3941 42 48 49 50 57 58 62 63 68 73 77 79 84 85 86 89 91 92 93 98 99 111112 117 126 131 134 137 139 142 145 146 147 148 150 151 154 156 157 1641 6 8 13 17 19 21 24 27 30 36 40 43 51 59 64 69 74 78 80 87 90 94 100113 118 127 132 135 138 140 143 149 152 155 158 165 2 9 14 22 25 28 4452 60 65 70 75 81 88 95 101 114 119 128 133 136 141 144 153 159 166 4653 54 61 66 97 103 107 108 109 120 121 124 129 130 167 10 15 45 71 76 8296 102 115 160 11 47 104 106 116 122 181 55 56 67 72 83 105 110 123 125161 162 163 168 169 170 171 172 173 174 175 176 177 178 179 180 182183]; (k) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40 4445 46 48 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87 89 90 91 9296 97 101 102 103 107 108 109 111 113 115 118 121 124 126 128 130 131133 135 138 139 140 142 143 146 147 149 152 154 158 159 160 3 5 8 11 1618 21 23 25 28 30 35 41 47 49 52 55 63 66 72 75 77 80 83 88 93 98 104110 112 114 116 119 122 125 127 129 132 134 136 141 144 148 150 153 155161 12 26 31 36 42 50 53 56 64 67 84 94 99 105 117 120 123 137 145 151156 162 13 32 33 38 43 58 59 100 157 165 37 60 95 166 68 169 57 106 163164 61 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182 183];(l) ϕ_(T)=[0 1 2 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40 44 45 4648 51 54 62 65 69 70 71 73 74 76 78 79 81 82 85 86 87 89 90 91 92 96 97101 102 103 107 108 109 111 113 115 118 121 124 126 128 130 131 133 135138 139 140 142 143 146 147 149 152 154 158 159 160 3 5 8 11 16 18 21 2325 28 30 35 41 47 49 52 55 63 66 72 75 77 80 83 88 93 98 104 110 112 114116 119 122 125 127 129 132 134 136 141 144 148 150 153 155 161 12 26 3136 42 50 53 56 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13 3233 37 38 43 57 58 59 60 61 68 95 100 106 157 163 164 165 166 167 168 169170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (m) ϕ_(T)=[0 12 4 6 7 9 10 14 15 17 19 20 22 24 27 29 34 39 40 44 45 46 48 51 54 62 6569 70 71 73 74 76 78 79 81 82 85 86 87 89 90 91 92 96 97 101 102 103 107108 109 111 113 115 118 121 124 126 128 130 131 133 135 138 139 140 142143 146 147 149 152 154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 4147 49 52 55 63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122125 127 129 132 134 136 141 144 148 150 153 155 161 12 26 31 36 42 50 5356 64 67 84 94 99 105 117 120 123 137 145 151 156 162 13 32 33 38 43 5859 100 157 165 37 57 60 61 68 95 106 163 164 166 167 168 169 170 171 172173 174 175 176 177 178 179 180 181 182 183]; (n) ϕ_(T)=[0 1 2 4 6 7 910 14 15 17 19 20 22 24 27 29 34 39 40 44 45 46 48 51 54 62 65 69 70 7173 74 76 78 79 81 82 85 86 87 89 90 91 92 96 97 101 102 103 107 108 109111 113 115 118 121 124 126 128 130 131 133 135 138 139 140 142 143 146147 149 152 154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 5255 63 66 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125 127 129132 134 136 141 144 148 150 153 155 161 12 26 31 36 42 50 53 56 64 67 8494 99 105 117 120 123 137 145 151 156 162 13 32 33 38 43 58 59 100 157165 37 60 95 166 57 61 68 106 163 164 167 168 169 170 171 172 173 174175 176 177 178 179 180 181 182 183]; (o) ϕ_(T)=[0 1 2 4 6 7 9 10 14 1517 19 20 22 24 27 29 34 39 40 44 45 46 48 51 54 62 65 69 70 71 73 74 7678 79 81 82 85 86 87 89 90 91 92 96 97 101 102 103 107 108 109 111 113115 118 121 124 126 128 130 131 133 135 138 139 140 142 143 146 147 149152 154 158 159 160 3 5 8 11 16 18 21 23 25 28 30 35 41 47 49 52 55 6366 72 75 77 80 83 88 93 98 104 110 112 114 116 119 122 125 127 129 132134 136 141 144 148 150 153 155 161 12 26 31 36 42 50 53 56 64 67 84 9499 105 117 120 123 137 145 151 156 162 13 32 33 38 43 58 59 100 157 16537 60 95 166 68 169 57 61 106 163 164 167 168 170 171 172 173 174 175176 177 178 179 180 181 182 183].
 12. The method of claim 4, whereinK_(max) is 160 and the template interleaver uses an interleaving patterncomprising any one of the following interleaving patterns, whereinindices corresponding to cyclic redundancy check (CRC) bits areunderlined: (a) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 3335 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 8081 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130 132135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 4 6 9 1115 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 9396 104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154 156161 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 147162 2 53 59 64 91 102 116 122 127 146 163 101 121 126 164 100 165 99 16698 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];(b) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66 6768 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111 117 118 120 121 122124 125 126 127 128 130 133 136 139 141 143 147 152 154 155 156 159 1641 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116119 123 129 132 135 138 140 142 146 151 153 158 165 0 6 15 18 23 26 3140 45 58 64 71 78 84 89 94 99 107 115 131 134 137 145 150 157 166 29 3035 38 39 50 51 52 56 62 93 98 105 106 113 167 44 57 63 77 83 88 114 144149 160 37 43 53 55 112 148 181 34 36 103 170 49 179 87 183 76 173 92163 54 171 178 180 182 104 161 162 168 169 172 174 175 176 177]; (c)ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139 137 135 132130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 7877 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 3129 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 160 156 154 151 148 143 141138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 6661 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122116 102 91 64 59 53 2 163 126 121 101 164 100 165 99 166 98 167 168 169170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (d) ϕ_(T)=[159156 155 154 152 147 143 141 139 136 133 130 128 127 126 125 124 122 121120 118 117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 6661 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 164 158 153 151146 142 140 138 135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 6559 46 41 32 27 24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 10799 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 9362 56 52 51 50 39 38 35 30 29 167 149 144 114 88 83 77 63 57 44 160 148112 55 53 43 37 181 103 36 34 170 49 179 87 183 76 173 92 163 54 171 178180 182 104 161 162 168 169 172 174 175 176 177]; (e) ϕ_(T)=[0 1 5 7 1012 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 5758 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105108 111 113 114 115 119 120 125 130 132 135 137 139 140 142 144 145 149150 152 153 155 157 158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 4043 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129131 134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60 6575 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91 98 99 100 101102 116 121 122 126 127 146 163 164 165 166 167 168 169 170 171 172 173174 175 176 177 178 179 180 181 182 183]; (f) ϕ_(T)=[2 3 5 8 9 11 12 1314 17 20 22 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 80 82 86 91 9697 101 102 109 110 111 117 118 120 121 122 124 125 126 127 128 130 133136 139 141 143 147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 3241 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99107 115 131 134 137 145 150 157 166 29 30 34 35 36 37 38 39 43 44 49 5051 52 53 54 55 56 57 62 63 76 77 83 87 88 92 93 98 103 104 105 106 112113 114 144 148 149 160 161 162 163 167 168 169 170 171 172 173 174 175176 177 178 179 180 181 182 183]; (g) ϕ_(T)=[159 158 157 155 153 152 150149 145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111 108105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 5756 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 107 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124 118 112 110107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 2725 23 18 15 11 9 6 4 161 147 133 128 123 117 109 106 103 95 92 75 65 6054 42 39 36 22 14 8 3 162 2 53 59 64 91 98 99 100 101 102 116 121 122126 127 146 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177178 179 180 181 182 183]; (h) ϕ_(T)=[159 156 155 154 152 147 143 141 139136 133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102 10197 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 1714 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132 129 123119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 16 10 74 1 165 157 150 145 137 134 131 115 107 99 94 89 84 78 71 64 58 45 40 3126 23 18 15 6 0 166 29 30 34 35 36 37 38 39 43 44 49 50 51 52 53 54 5556 57 62 63 76 77 83 87 88 92 93 98 103 104 105 106 112 113 114 144 148149 160 161 162 163 167 168 169 170 171 172 173 174 175 176 177 178 179180 181 182 183]; (i) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 2931 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 7778 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130132 135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 4 69 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 8487 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133147 162 2 53 59 64 91 102 116 122 127 146 163 98 99 100 101 121 126 164165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (j) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60 6166 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111 117 118 120121 122 124 125 126 127 128 130 133 136 139 141 143 147 152 154 155 156159 164 1 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100108 116 119 123 129 132 135 138 140 142 146 151 153 158 165 0 6 15 18 2326 31 40 45 58 64 71 78 84 89 94 99 107 115 131 134 137 145 150 157 16629 30 35 38 39 50 51 52 56 62 93 98 105 106 113 167 34 36 37 43 44 49 5354 55 57 63 76 77 83 87 88 92 103 104 112 114 144 148 149 160 161 162163 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183];(k) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139 137 135132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 8180 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 3533 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 160 156 154 151 148143 141 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 7671 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146127 122 116 102 91 64 59 53 2 163 98 99 100 101 121 126 164 165 166 167168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (l)ϕ_(T)=[159 156 155 154 152 147 143 141 139 136 133 130 128 127 126 125124 122 121 120 118 117 111 110 109 102 101 97 96 91 86 82 80 75 74 7370 68 67 66 61 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 164158 153 151 146 142 140 138 135 132 129 123 119 116 108 100 95 90 85 8179 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1 165 157 150 145 137 134131 115 107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106105 98 93 62 56 52 51 50 39 38 35 30 29 167 34 36 37 43 44 49 53 54 5557 63 76 77 83 87 88 92 103 104 112 114 144 148 149 160 161 162 163 168169 170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (m)ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 4648 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 8889 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137 139 140142 144 145 149 150 152 153 155 157 158 159 160 4 6 9 11 15 18 23 25 2730 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110112 118 124 129 131 134 136 138 141 143 148 151 154 156 161 3 8 14 22 3639 42 54 60 65 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 6491 102 116 122 127 146 163 101 121 126 164 98 99 100 165 166 167 168 169170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (n) ϕ_(T)=[2 35 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66 67 68 70 73 74 7580 82 86 91 96 97 101 102 109 110 111 117 118 120 121 122 124 125 126127 128 130 133 136 139 141 143 147 152 154 155 156 159 164 1 4 7 10 1619 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129132 135 138 140 142 146 151 153 158 165 0 6 15 18 23 26 31 40 45 58 6471 78 84 89 94 99 107 115 131 134 137 145 150 157 166 29 30 35 38 39 5051 52 56 62 93 98 105 106 113 167 44 57 63 77 83 88 114 144 149 160 3436 37 43 49 53 54 55 76 87 92 103 104 112 148 161 162 163 168 169 170171 172 173 174 175 176 177 178 179 180 181 182 183]; (o) ϕ_(T)=[159 158157 155 153 152 150 149 145 144 142 140 139 137 135 132 130 125 120 119115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 7069 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 2120 19 17 16 13 12 10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 4340 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117 109 106103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 122 116 102 91 6459 53 2 163 126 121 101 164 98 99 100 165 166 167 168 169 170 171 172173 174 175 176 177 178 179 180 181 182 183]; (p) ϕ_(T)=[159 156 155 154152 147 143 141 139 136 133 130 128 127 126 125 124 122 121 120 118 117111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 4742 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 164 158 153 151 146 142 140138 135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 3227 24 21 19 16 10 7 4 1 165 157 150 145 137 134 131 115 107 99 94 89 8478 71 64 58 45 40 31 26 23 18 15 6 0 166 113 106 105 98 93 62 56 52 5150 39 38 35 30 29 167 149 144 114 88 83 77 63 57 44 160 34 36 37 43 4953 54 55 76 87 92 103 104 112 148 161 162 163 168 169 170 171 172 173174 175 176 177 178 179 180 181 182 183]; (q) ϕ_(T)=[0 1 5 7 10 12 13 1617 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 6367 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113114 115 119 120 125 130 132 135 137 139 140 142 144 145 149 150 152 153155 157 158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 4955 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 147 162 2 53 59 64 91 102 116 122 127 146 163101 121 126 164 100 165 98 99 166 167 168 169 170 171 172 173 174 175176 177 178 179 180 181 182 183]; (r) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 2022 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 80 82 86 91 96 97 101102 109 110 111 117 118 120 121 122 124 125 126 127 128 130 133 136 139141 143 147 152 154 155 156 159 164 1 4 7 10 16 19 21 24 27 32 41 46 5965 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140 142 146151 153 158 165 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99 107 115131 134 137 145 150 157 166 29 30 35 38 39 50 51 52 56 62 93 98 105 106113 167 44 57 63 77 83 88 114 144 149 160 37 43 53 55 112 148 181 34 3649 54 76 87 92 103 104 161 162 163 168 169 170 171 172 173 174 175 176177 178 179 180 182 183]; (s) ϕ_(T)=[159 158 157 155 153 152 150 149 145144 142 140 139 137 135 132 130 125 120 119 115 114 113 111 108 105 9794 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 5251 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 10 160 156 154 151 148 143 141 138 136 134 131 129 124 118 112 110 107104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 2318 15 11 9 6 4 161 147 133 128 123 117 109 106 103 95 92 75 65 60 54 4239 36 22 14 8 3 162 146 127 122 116 102 91 64 59 53 2 163 126 121 101164 100 165 98 99 166 167 168 169 170 171 172 173 174 175 176 177 178179 180 181 182 183]; (t) ϕ_(T)=[159 156 155 154 152 147 143 141 139 136133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102 101 9796 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17 1413 12 11 9 8 5 3 2 164 158 153 151 146 142 140 138 135 132 129 123 119116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1165 157 150 145 137 134 131 115 107 99 94 89 84 78 71 64 58 45 40 31 2623 18 15 6 0 166 113 106 105 98 93 62 56 52 51 50 39 38 35 30 29 167 149144 114 88 83 77 63 57 44 160 148 112 55 53 43 37 181 34 36 49 54 76 8792 103 104 161 162 163 168 169 170 171 172 173 174 175 176 177 178 179180 182 183]; (u) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 3133 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 7880 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130132 135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 4 69 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 8487 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133147 162 2 59 100 101 116 121 126 127 146 165 64 99 122 166 91 169 53 102163 164 98 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (v) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 3841 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 8385 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137139 140 142 144 145 149 150 152 153 155 157 158 159 160 4 6 9 11 15 1823 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104107 110 112 118 124 129 131 134 136 138 141 143 148 151 154 156 161 3 814 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 147 162 259 100 101 116 121 126 127 146 165 64 99 122 166 91 169 53 102 163 16498 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (w)ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139 137 135 132130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 7877 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 3129 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 160 156 154 151 148 143 141138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 6661 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162 146 127 126121 116 101 100 59 2 165 122 99 64 166 91 169 102 53 163 164 98 167 168170 171 172 173 174 175 176 177 178 179 180 181 182 183]; (x) ϕ_(T)=[0 15 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 5256 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97105 108 111 113 114 115 119 120 125 130 132 135 137 139 140 142 144 145149 150 152 153 155 157 158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 3740 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124129 131 134 136 138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 6065 75 92 95 103 106 109 117 123 128 133 147 162 2 53 59 64 91 98 99 100101 102 116 121 122 126 127 146 163 164 165 166 167 168 169 170 171 172173 174 175 176 177 178 179 180 181 182 183]; (y) ϕ_(T)=[159 158 157 155153 152 150 149 145 144 142 140 139 137 135 132 130 125 120 119 115 114113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 6763 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 1716 13 12 10 7 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 3734 32 30 27 25 23 18 15 11 9 6 4 161 147 133 128 123 117 109 106 103 9592 75 65 60 54 42 39 36 22 14 8 3 162 2 53 59 64 91 98 99 100 101 102116 121 122 126 127 146 163 164 165 166 167 168 169 170 171 172 173 174175 176 177 178 179 180 181 182 183]; (z) ϕ_(T)=[0 1 5 7 10 12 13 16 1719 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 6768 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113114 115 119 120 125 130 132 135 137 139 140 142 144 145 149 150 152 153155 157 158 159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 4955 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136138 141 143 148 151 154 156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 147 162 2 59 100 101 116 121 126 127 146 165 5364 91 98 99 102 122 163 164 166 167 168 169 170 171 172 173 174 175 176177 178 179 180 181 182 183]; (aa) ϕ_(T)=[159 158 157 155 153 152 150149 145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111 108105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 5756 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 107 5 1 0 160 156 154 151 148 143 141 138 136 134 131 129 124 118 112 110107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 2725 23 18 15 11 9 6 4 161 147 133 128 123 117 109 106 103 95 92 75 65 6054 42 39 36 22 14 8 3 162 146 127 126 121 116 101 100 59 2 165 53 64 9198 99 102 122 163 164 166 167 168 169 170 171 172 173 174 175 176 177178 179 180 181 182 183]; (bb) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 2426 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 7273 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119120 125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157 158159 160 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 7176 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143148 151 154 156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117123 128 133 147 162 2 59 100 101 116 121 126 127 146 165 64 99 122 16653 91 98 102 163 164 167 168 169 170 171 172 173 174 175 176 177 178 179180 181 182 183]; (cc) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144142 140 139 137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 9089 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 5048 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 160156 154 151 148 143 141 138 136 134 131 129 124 118 112 110 107 104 9693 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 1511 9 6 4 161 147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 3622 14 8 3 162 146 127 126 121 116 101 100 59 2 165 122 99 64 166 53 9198 102 163 164 167 168 169 170 171 172 173 174 175 176 177 178 179 180181 182 183]; (dd) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 3133 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 7880 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130132 135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 4 69 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 8487 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154156 161 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133147 162 2 59 100 101 116 121 126 127 146 165 64 99 122 166 91 169 53 98102 163 164 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182183]; (ee) ϕ_(T)=[159 158 157 155 153 152 150 149 145 144 142 140 139137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 8583 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 4138 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 160 156 154 151148 143 141 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 8279 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 161147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 162146 127 126 121 116 101 100 59 2 165 122 99 64 166 91 169 53 98 102 163164 167 168 170 171 172 173 174 175 176 177 178 179 180 181 182 183].13. The method of claim 3, wherein K_(max) is 200 and the templateinterleaver uses an interleaving pattern comprising any one of thefollowing interleaving patterns, wherein indices corresponding to cyclicredundancy check (CRC) bits are underlined: (a) ϕ_(T)=[0 1 2 3 9 10 1216 20 21 23 26 27 29 31 34 36 38 39 40 43 44 45 47 52 56 58 60 63 66 6971 72 73 74 75 77 78 79 81 82 88 89 90 97 98 102 103 108 113 117 119 124125 126 129 131 132 133 138 139 151 152 157 166 171 174 177 179 182 185186 187 188 190 191 194 196 197 204 4 11 13 17 22 24 28 30 32 35 37 4146 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118 120 127 130134 140 153 158 167 172 175 178 180 183 189 192 195 198 205 5 14 18 2533 42 49 54 62 65 68 84 92 100 105 110 115 121 128 135 141 154 159 168173 176 181 184 193 199 206 8 15 86 93 94 101 106 137 143 147 148 149160 161 164 169 170 207 6 19 50 55 85 111 116 122 136 142 155 200 87 95107 144 150 162 165 208 51 156 214 7 146 221 163 219 96 210 145 202 212112 211 216 223 123 201 203 209 213 215 217 218 220 222]; (b) ϕ_(T)=[0 12 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39 40 43 44 45 47 52 56 5860 63 66 69 71 72 73 74 75 77 78 79 81 82 88 89 90 97 98 102 103 108 113117 119 124 125 126 129 131 132 133 138 139 151 152 157 166 171 174 177179 182 185 186 187 188 190 191 194 196 197 204 4 11 13 17 22 24 28 3032 35 37 41 46 48 53 57 59 61 64 67 70 76 80 83 91 99 104 109 114 118120 127 130 134 140 153 158 167 172 175 178 180 183 189 192 195 198 2055 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121 128 135 141154 159 168 173 176 181 184 193 199 206 6 7 8 15 19 50 51 55 85 86 87 9394 95 96 101 106 107 111 112 116 122 123 136 137 142 143 144 145 146 147148 149 150 155 156 160 161 162 163 164 165 169 170 200 201 202 203 207208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (c)ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 39 40 43 44 4547 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81 82 88 89 90 97 98 102103 108 113 117 119 124 125 126 129 131 132 133 138 139 151 152 157 166171 174 177 179 182 185 186 187 188 190 191 194 196 197 204 4 11 13 1722 24 28 30 32 35 37 41 46 48 53 57 59 61 64 67 70 76 80 83 91 99 104109 114 118 120 127 130 134 140 153 158 167 172 175 178 180 183 189 192195 198 205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105 110 115 121128 135 141 154 159 168 173 176 181 184 193 199 206 8 15 86 93 94 101106 137 143 147 148 149 160 161 164 169 170 207 6 7 19 50 51 55 85 87 9596 107 111 112 116 122 123 136 142 144 145 146 150 155 156 162 163 165200 201 202 203 208 209 210 211 212 213 214 215 216 217 218 219 220 221222 223]; (d) ϕ_(T)=[0 1 2 3 9 10 12 16 20 21 23 26 27 29 31 34 36 38 3940 43 44 45 47 52 56 58 60 63 66 69 71 72 73 74 75 77 78 79 81 82 88 8990 97 98 102 103 108 113 117 119 124 125 126 129 131 132 133 138 139 151152 157 166 171 174 177 179 182 185 186 187 188 190 191 194 196 197 2044 11 13 17 22 24 28 30 32 35 37 41 46 48 53 57 59 61 64 67 70 76 80 8391 99 104 109 114 118 120 127 130 134 140 153 158 167 172 175 178 180183 189 192 195 198 205 5 14 18 25 33 42 49 54 62 65 68 84 92 100 105110 115 121 128 135 141 154 159 168 173 176 181 184 193 199 206 8 15 8693 94 101 106 137 143 147 148 149 160 161 164 169 170 207 6 19 50 55 85111 116 122 136 142 155 200 7 51 87 95 96 107 112 123 144 145 146 150156 162 163 165 201 202 203 208 209 210 211 212 213 214 215 216 217 218219 220 221 222 223]; (e) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 2832 33 35 37 38 39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 7479 80 84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121 122125 126 127 129 130 131 132 136 137 141 142 143 147 148 149 151 153 155158 161 164 166 168 170 171 173 175 178 179 180 182 183 186 187 189 192194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 48 51 56 58 61 6365 68 70 75 81 87 89 92 95 103 106 112 115 117 120 123 128 133 138 144150 152 154 156 159 162 165 167 169 172 174 176 181 184 188 190 193 195201 10 15 18 26 30 52 66 71 76 82 90 93 96 104 107 124 134 139 145 157160 163 177 185 191 196 202 27 31 53 72 77 83 97 108 135 140 146 197 20373 78 98 204 99 205 100 206 101 207 208 209 210 211 212 213 214 215 216217 218 219 220 221 222 223]; (f) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 2022 24 28 32 33 35 37 38 39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 6467 69 74 79 80 84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119121 122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149 151153 155 158 161 164 166 168 170 171 173 175 178 179 180 182 183 186 187189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 48 51 5658 61 63 65 68 70 75 81 87 89 92 95 103 106 112 115 117 120 123 128 133138 144 150 152 154 156 159 162 165 167 169 172 174 176 181 184 188 190193 195 201 10 15 18 26 30 52 66 71 76 82 90 93 96 104 107 124 134 139145 157 160 163 177 185 191 196 202 27 31 53 72 73 77 78 83 97 98 99 100101 108 135 140 146 197 203 204 205 206 207 208 209 210 211 212 213 214215 216 217 218 219 220 221 222 223]; (g) ϕ_(T)=[0 2 3 5 6 8 11 12 13 1619 20 22 24 28 32 33 35 37 38 39 40 41 42 44 46 47 49 50 54 55 57 59 6062 64 67 69 74 79 80 84 85 86 88 91 94 102 105 109 110 111 113 114 116118 119 121 122 125 126 127 129 130 131 132 136 137 141 142 143 147 148149 151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182 183186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 4851 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106 112 115 117 120 123128 133 138 144 150 152 154 156 159 162 165 167 169 172 174 176 181 184188 190 193 195 201 10 15 18 26 30 52 66 71 76 82 90 93 96 104 107 124134 139 145 157 160 163 177 185 191 196 202 27 31 53 72 77 83 97 108 135140 146 197 203 73 78 98 99 100 101 204 205 206 207 208 209 210 211 212213 214 215 216 217 218 219 220 221 222 223]; (h) ϕ_(T)=[0 2 3 5 6 8 1112 13 16 19 20 22 24 28 32 33 35 37 38 39 40 41 42 44 46 47 49 50 54 5557 59 60 62 64 67 69 74 79 80 84 85 86 88 91 94 102 105 109 110 111 113114 116 118 119 121 122 125 126 127 129 130 131 132 136 137 141 142 143147 148 149 151 153 155 158 161 164 166 168 170 171 173 175 178 179 180182 183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 3643 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106 112 115 117120 123 128 133 138 144 150 152 154 156 159 162 165 167 169 172 174 176181 184 188 190 193 195 201 10 15 18 26 30 52 66 71 76 82 90 93 96 104107 124 134 139 145 157 160 163 177 185 191 196 202 27 31 53 72 77 83 97108 135 140 146 197 203 73 78 98 204 99 100 101 205 206 207 208 209 210211 212 213 214 215 216 217 218 219 220 221 222 223]; (i) ϕ_(T)=[0 2 3 56 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38 39 40 41 42 44 46 47 49 5054 55 57 59 60 62 64 67 69 74 79 80 84 85 86 88 91 94 102 105 109 110111 113 114 116 118 119 121 122 125 126 127 129 130 131 132 136 137 141142 143 147 148 149 151 153 155 158 161 164 166 168 170 171 173 175 178179 180 182 183 186 187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 2529 34 36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95 103 106 112115 117 120 123 128 133 138 144 150 152 154 156 159 162 165 167 169 172174 176 181 184 188 190 193 195 201 10 15 18 26 30 52 66 71 76 82 90 9396 104 107 124 134 139 145 157 160 163 177 185 191 196 202 27 31 53 7277 83 97 108 135 140 146 197 203 73 78 98 204 99 205 100 101 206 207 208209 210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (j)ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 38 39 40 41 4244 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80 84 85 86 88 91 94 102105 109 110 111 113 114 116 118 119 121 122 125 126 127 129 130 131 132136 137 141 142 143 147 148 149 151 153 155 158 161 164 166 168 170 171173 175 178 179 180 182 183 186 187 189 192 194 198 199 200 1 4 7 9 1417 21 23 25 29 34 36 43 45 48 51 56 58 61 63 65 68 70 75 81 87 89 92 95103 106 112 115 117 120 123 128 133 138 144 150 152 154 156 159 162 165167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 26 30 52 66 7176 82 90 93 96 104 107 124 134 139 145 157 160 163 177 185 191 196 20227 53 72 73 78 83 98 99 140 197 205 31 77 100 135 206 108 209 97 146 203204 101 207 208 210 211 212 213 214 215 216 217 218 219 220 221 222223]; (k) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 35 37 3839 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80 84 85 8688 91 94 102 105 109 110 111 113 114 116 118 119 121 122 125 126 127 129130 131 132 136 137 141 142 143 147 148 149 151 153 155 158 161 164 166168 170 171 173 175 178 179 180 182 183 186 187 189 192 194 198 199 2001 4 7 9 14 17 21 23 25 29 34 36 43 45 48 51 56 58 61 63 65 68 70 75 8187 89 92 95 103 106 112 115 117 120 123 128 133 138 144 150 152 154 156159 162 165 167 169 172 174 176 181 184 188 190 193 195 201 10 15 18 2630 52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163 177 185191 196 202 27 31 53 72 73 77 78 83 97 98 99 100 101 108 135 140 146 197203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220221 222 223]; (l) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 28 32 33 3537 38 39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 74 79 80 8485 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121 122 125 126127 129 130 131 132 136 137 141 142 143 147 148 149 151 153 155 158 161164 166 168 170 171 173 175 178 179 180 182 183 186 187 189 192 194 198199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 48 51 56 58 61 63 65 68 7075 81 87 89 92 95 103 106 112 115 117 120 123 128 133 138 144 150 152154 156 159 162 165 167 169 172 174 176 181 184 188 190 193 195 201 1015 18 26 30 52 66 71 76 82 90 93 96 104 107 124 134 139 145 157 160 163177 185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77 97 100 101108 135 146 203 204 206 207 208 209 210 211 212 213 214 215 216 217 218219 220 221 222 223]; (m) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 19 20 22 24 2832 33 35 37 38 39 40 41 42 44 46 47 49 50 54 55 57 59 60 62 64 67 69 7479 80 84 85 86 88 91 94 102 105 109 110 111 113 114 116 118 119 121 122125 126 127 129 130 131 132 136 137 141 142 143 147 148 149 151 153 155158 161 164 166 168 170 171 173 175 178 179 180 182 183 186 187 189 192194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 48 51 56 58 61 6365 68 70 75 81 87 89 92 95 103 106 112 115 117 120 123 128 133 138 144150 152 154 156 159 162 165 167 169 172 174 176 181 184 188 190 193 195201 10 15 18 26 30 52 66 71 76 82 90 93 96 104 107 124 134 139 145 157160 163 177 185 191 196 202 27 53 72 73 78 83 98 99 140 197 205 31 77100 135 206 97 101 108 146 203 204 207 208 209 210 211 212 213 214 215216 217 218 219 220 221 222 223]; (n) ϕ_(T)=[0 2 3 5 6 8 11 12 13 16 1920 22 24 28 32 33 35 37 38 39 40 41 42 44 46 47 49 50 54 55 57 59 60 6264 67 69 74 79 80 84 85 86 88 91 94 102 105 109 110 111 113 114 116 118119 121 122 125 126 127 129 130 131 132 136 137 141 142 143 147 148 149151 153 155 158 161 164 166 168 170 171 173 175 178 179 180 182 183 186187 189 192 194 198 199 200 1 4 7 9 14 17 21 23 25 29 34 36 43 45 48 5156 58 61 63 65 68 70 75 81 87 89 92 95 103 106 112 115 117 120 123 128133 138 144 150 152 154 156 159 162 165 167 169 172 174 176 181 184 188190 193 195 201 10 15 18 26 30 52 66 71 76 82 90 93 96 104 107 124 134139 145 157 160 163 177 185 191 196 202 27 53 72 73 78 83 98 99 140 197205 31 77 100 135 206 108 209 97 101 146 203 204 207 208 210 211 212 213214 215 216 217 218 219 220 221 222 223]; (o) ϕ_(T)=[0 1 4 5 9 11 12 1718 19 21 24 26 28 31 34 41 42 47 52 54 57 63 64 68 69 70 71 72 73 74 7678 79 83 85 89 90 97 98 99 102 103 104 106 108 109 110 114 116 118 120121 122 123 125 128 129 132 135 137 141 142 144 148 152 156 158 160 161162 163 164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194196 197 212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62 65 84 8893 95 101 107 111 112 113 115 119 126 127 131 136 139 145 146 151 159168 169 173 175 184 185 186 193 199 215 3 10 14 16 23 29 30 37 40 43 5556 67 75 77 81 100 117 124 147 150 167 176 182 190 198 204 33 44 87 9194 134 153 154 155 157 165 207 53 61 66 80 138 195 211 82 96 105 140 143170 218 6 39 86 92 208 15 22 183 200 49 130 210 149 203 48 202 59 201209 214 133 205 206 213 216 217]; (p) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 2124 26 28 31 34 41 42 47 52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 8385 89 90 97 98 99 102 103 104 106 108 109 110 114 116 118 120 121 122123 125 128 129 132 135 137 141 142 144 148 152 156 158 160 161 162 163164 166 171 172 174 177 178 179 180 181 187 188 189 191 192 194 196 197212 2 7 8 13 20 25 27 32 35 36 38 45 46 50 51 58 60 62 65 84 88 93 95101 107 111 112 113 115 119 126 127 131 136 139 145 146 151 159 168 169173 175 184 185 186 193 199 215 3 10 14 16 23 29 30 37 40 43 55 56 67 7577 81 100 117 124 147 150 167 176 182 190 198 204 6 15 22 33 39 44 48 4953 59 61 66 80 82 86 87 91 92 94 96 105 130 133 134 138 140 143 149 153154 155 157 165 170 183 195 200 201 202 203 205 206 207 208 209 210 211213 214 216 217 218]; (q) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 3134 41 42 47 52 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 9798 99 102 103 104 106 108 109 110 114 116 118 120 121 122 123 125 128129 132 135 137 141 142 144 148 152 156 158 160 161 162 163 164 166 171172 174 177 178 179 180 181 187 188 189 191 192 194 196 197 212 2 7 8 1320 25 27 32 35 36 38 45 46 50 51 58 60 62 65 84 88 93 95 101 107 111 112113 115 119 126 127 131 136 139 145 146 151 159 168 169 173 175 184 185186 193 199 215 3 10 14 16 23 29 30 37 40 43 55 56 67 75 77 81 100 117124 147 150 167 176 182 190 198 204 33 44 87 91 94 134 153 154 155 157165 207 6 15 22 39 48 49 53 59 61 66 80 82 86 92 96 105 130 133 138 140143 149 170 183 195 200 201 202 203 205 206 208 209 210 211 213 214 216217 218]; (r) ϕ_(T)=[0 1 4 5 9 11 12 17 18 19 21 24 26 28 31 34 41 42 4752 54 57 63 64 68 69 70 71 72 73 74 76 78 79 83 85 89 90 97 98 99 102103 104 106 108 109 110 114 116 118 120 121 122 123 125 128 129 132 135137 141 142 144 148 152 156 158 160 161 162 163 164 166 171 172 174 177178 179 180 181 187 188 189 191 192 194 196 197 212 2 7 8 13 20 25 27 3235 36 38 45 46 50 51 58 60 62 65 84 88 93 95 101 107 111 112 113 115 119126 127 131 136 139 145 146 151 159 168 169 173 175 184 185 186 193 199215 3 10 14 16 23 29 30 37 40 43 55 56 67 75 77 81 100 117 124 147 150167 176 182 190 198 204 33 44 87 91 94 134 153 154 155 157 165 207 53 6166 80 138 195 211 6 15 22 39 48 49 59 82 86 92 96 105 130 133 140 143149 170 183 200 201 202 203 205 206 208 209 210 213 214 216 217 218].14. The method of claim 4, wherein K_(max) is 200 and the templateinterleaver uses an interleaving pattern comprising any one of thefollowing interleaving patterns, wherein indices corresponding to cyclicredundancy check (CRC) bits are underlined: (a) ϕ_(T)=[2 3 5 8 9 11 1213 14 17 20 22 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 80 82 86 9196 97 101 102 109 110 111 117 118 120 121 122 124 125 126 127 128 130133 136 139 141 143 147 152 154 155 156 159 160 161 163 165 168 170 172173 176 178 179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 2427 32 41 46 59 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135138 140 142 146 151 153 158 162 164 167 169 171 175 177 182 186 188 195205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 89 94 99 107 115 131 134 137145 150 157 166 174 181 185 194 206 29 30 35 38 39 50 51 52 56 62 93 98105 106 113 184 191 207 44 57 63 77 83 88 114 144 149 180 193 200 34 3749 55 92 104 112 208 43 148 214 53 192 221 36 219 103 210 54 202 212 87211 216 223 76 201 203 209 213 215 217 218 220 222]; (b) ϕ_(T)=[199 198197 196 190 189 187 183 179 178 176 173 172 170 168 165 163 161 160 159156 155 154 152 147 143 141 139 136 133 130 128 127 126 125 124 122 121120 118 117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 6661 60 48 47 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186182 177 175 171 169 167 164 162 158 153 151 146 142 140 138 135 132 129123 119 116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 1610 7 4 1 205 194 185 181 174 166 157 150 145 137 134 131 115 107 99 9489 84 78 71 64 58 45 40 31 26 23 18 15 6 0 206 191 184 113 106 105 98 9362 56 52 51 50 39 38 35 30 29 207 193 180 149 144 114 88 83 77 63 57 44200 112 104 92 55 49 37 34 208 148 43 214 192 53 221 36 219 103 210 54212 202 87 211 216 223 76 215 213 217 218 201 220 203 222 209]; (c)ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 42 47 48 60 61 66 67 6870 73 74 75 80 82 86 91 96 97 101 102 109 110 111 117 118 120 121 122124 125 126 127 128 130 133 136 139 141 143 147 152 154 155 156 159 160161 163 165 168 170 172 173 176 178 179 183 187 189 190 196 197 198 199204 1 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 79 81 85 90 95 100 108116 119 123 129 132 135 138 140 142 146 151 153 158 162 164 167 169 171175 177 182 186 188 195 205 0 6 15 18 23 26 31 40 45 58 64 71 78 84 8994 99 107 115 131 134 137 145 150 157 166 174 181 185 194 206 29 30 3435 36 37 38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77 83 87 88 9293 98 103 104 105 106 112 113 114 144 148 149 180 184 191 192 193 200201 202 203 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221222 223]; (d) ϕ_(T)=[199 198 197 196 190 189 187 183 179 178 176 173 172170 168 165 163 161 160 159 156 155 154 152 147 143 141 139 136 133 130128 127 126 125 124 122 121 120 118 117 111 110 109 102 101 97 96 91 8682 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 20 17 14 13 12 119 8 5 3 2 204 195 188 186 182 177 175 171 169 167 164 162 158 153 151146 142 140 138 135 132 129 123 119 116 108 100 95 90 85 81 79 72 69 6559 46 41 32 27 24 21 19 16 10 7 4 1 205 194 185 181 174 166 157 150 145137 134 131 115 107 99 94 89 84 78 71 64 58 45 40 31 26 23 18 15 6 0 20629 30 34 35 36 37 38 39 43 44 49 50 51 52 53 54 55 56 57 62 63 76 77 8387 88 92 93 98 103 104 105 106 112 113 114 144 148 149 180 184 191 192193 200 201 202 203 207 208 209 210 211 212 213 214 215 216 217 218 219220 221 222 223]; (e) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 20 22 25 28 33 4247 48 60 61 66 67 68 70 73 74 75 80 82 86 91 96 97 101 102 109 110 111117 118 120 121 122 124 125 126 127 128 130 133 136 139 141 143 147 152154 155 156 159 160 161 163 165 168 170 172 173 176 178 179 183 187 189190 196 197 198 199 204 1 4 7 10 16 19 21 24 27 32 41 46 59 65 69 72 7981 85 90 95 100 108 116 119 123 129 132 135 138 140 142 146 151 153 158162 164 167 169 171 175 177 182 186 188 195 205 0 6 15 18 23 26 31 40 4558 64 71 78 84 89 94 99 107 115 131 134 137 145 150 157 166 174 181 185194 206 29 30 35 38 39 50 51 52 56 62 93 98 105 106 113 184 191 207 3436 37 43 44 49 53 54 55 57 63 76 77 83 87 88 92 103 104 112 114 144 148149 180 192 193 200 201 202 203 208 209 210 211 212 213 214 215 216 217218 219 220 221 222 223]; (f) ϕ_(T)=[199 198 197 196 190 189 187 183 179178 176 173 172 170 168 165 163 161 160 159 156 155 154 152 147 143 141139 136 133 130 128 127 126 125 124 122 121 120 118 117 111 110 109 102101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 48 47 42 33 28 25 22 2017 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177 175 171 169 167 164 162158 153 151 146 142 140 138 135 132 129 123 119 116 108 100 95 90 85 8179 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1 205 194 185 181 174 166157 150 145 137 134 131 115 107 99 94 89 84 78 71 64 58 45 40 31 26 2318 15 6 0 206 191 184 113 106 105 98 93 62 56 52 51 50 39 38 35 30 29207 34 36 37 43 44 49 53 54 55 57 63 76 77 83 87 88 92 103 104 112 114144 148 149 180 192 193 200 201 202 203 208 209 210 211 212 213 214 215216 217 218 219 220 221 222 223]; (g) ϕ_(T)=[2 3 5 8 9 11 12 13 14 17 2022 25 28 33 42 47 48 60 61 66 67 68 70 73 74 75 80 82 86 91 96 97 101102 109 110 111 117 118 120 121 122 124 125 126 127 128 130 133 136 139141 143 147 152 154 155 156 159 160 161 163 165 168 170 172 173 176 178179 183 187 189 190 196 197 198 199 204 1 4 7 10 16 19 21 24 27 32 41 4659 65 69 72 79 81 85 90 95 100 108 116 119 123 129 132 135 138 140 142146 151 153 158 162 164 167 169 171 175 177 182 186 188 195 205 0 6 1518 23 26 31 40 45 58 64 71 78 84 89 94 99 107 115 131 134 137 145 150157 166 174 181 185 194 206 29 30 35 38 39 50 51 52 56 62 93 98 105 106113 184 191 207 44 57 63 77 83 88 114 144 149 180 193 200 34 36 37 43 4953 54 55 76 87 92 103 104 112 148 192 201 202 203 208 209 210 211 212213 214 215 216 217 218 219 220 221 222 223]; (h) ϕ_(T)=[199 198 197 196190 189 187 183 179 178 176 173 172 170 168 165 163 161 160 159 156 155154 152 147 143 141 139 136 133 130 128 127 126 125 124 122 121 120 118117 111 110 109 102 101 97 96 91 86 82 80 75 74 73 70 68 67 66 61 60 4847 42 33 28 25 22 20 17 14 13 12 11 9 8 5 3 2 204 195 188 186 182 177175 171 169 167 164 162 158 153 151 146 142 140 138 135 132 129 123 119116 108 100 95 90 85 81 79 72 69 65 59 46 41 32 27 24 21 19 16 10 7 4 1205 194 185 181 174 166 157 150 145 137 134 131 115 107 99 94 89 84 7871 64 58 45 40 31 26 23 18 15 6 0 206 191 184 113 106 105 98 93 62 56 5251 50 39 38 35 30 29 207 193 180 149 144 114 88 83 77 63 57 44 200 34 3637 43 49 53 54 55 76 87 92 103 104 112 148 192 201 202 203 208 209 210211 212 213 214 215 216 217 218 219 220 221 222 223]; (i) ϕ_(T)=[0 1 5 710 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 5657 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105108 111 113 114 115 119 120 125 130 132 135 137 139 140 142 144 145 149150 152 153 155 157 158 159 160 161 162 164 166 167 171 175 177 179 180183 186 187 188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 3032 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112118 124 129 131 134 136 138 141 143 148 151 154 156 163 165 170 174 176178 182 185 190 192 195 198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 147 169 173 181 184 189 202 2 53 59 64 91 102116 122 127 146 168 172 203 101 121 126 204 100 205 99 206 98 207 208209 210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (j)ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177 175 171 167166 164 162 161 160 159 158 157 155 153 152 150 149 145 144 142 140 139137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 8583 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 4138 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 200 198 195 192190 185 182 178 176 174 170 165 163 156 154 151 148 143 141 138 136 134131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 4745 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169 147133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 202 172168 146 127 122 116 102 91 64 59 53 2 203 126 121 101 204 100 205 99 20698 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223];(k) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 4446 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 8688 89 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137 139140 142 144 145 149 150 152 153 155 157 158 159 160 161 162 164 166 167171 175 177 179 180 183 186 187 188 191 193 194 196 197 199 200 4 6 9 1115 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 9396 104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154 156163 165 170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 4254 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173 181 184 189202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 146 168 172 203204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221222 223]; (l) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177175 171 167 166 164 162 161 160 159 158 157 155 153 152 150 149 145 144142 140 139 137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 9089 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 5048 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 200198 195 192 190 185 182 178 176 174 170 165 163 156 154 151 148 143 141138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 6661 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181173 169 147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 148 3 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 146 168 172203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220221 222 223]; (m) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 3133 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 7880 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130132 135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 161162 164 166 167 171 175 177 179 180 183 186 187 188 191 193 194 196 197199 200 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 7176 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143148 151 154 156 163 165 170 174 176 178 182 185 190 192 195 198 201 3 814 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173181 184 189 202 2 53 59 64 91 102 116 122 127 146 168 172 203 98 99 100101 121 126 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218219 220 221 222 223]; (n) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183180 179 177 175 171 167 166 164 162 161 160 159 158 157 155 153 152 150149 145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111 108105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 5756 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 107 5 1 0 200 198 195 192 190 185 182 178 176 174 170 165 163 156 154 151148 143 141 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 8279 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201189 184 181 173 169 147 133 128 123 117 109 106 103 95 92 75 65 60 54 4239 36 22 14 8 3 202 172 168 146 127 122 116 102 91 64 59 53 2 203 98 99100 101 121 126 204 205 206 207 208 209 210 211 212 213 214 215 216 217218 219 220 221 222 223]; (o) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 2426 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 7273 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119120 125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157 158159 160 161 162 164 166 167 171 175 177 179 180 183 186 187 188 191 193194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 4955 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136138 141 143 148 151 154 156 163 165 170 174 176 178 182 185 190 192 195198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133147 169 173 181 184 189 202 2 53 59 64 91 102 116 122 127 146 168 172203 101 121 126 204 98 99 100 205 206 207 208 209 210 211 212 213 214215 216 217 218 219 220 221 222 223]; (p) ϕ_(T)=[199 197 196 194 193 191188 187 186 183 180 179 177 175 171 167 166 164 162 161 160 159 158 157155 153 152 150 149 145 144 142 140 139 137 135 132 130 125 120 119 115114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 6968 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 2019 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176 174 170165 163 156 154 151 148 143 141 138 136 134 131 129 124 118 112 110 107104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 2318 15 11 9 6 4 201 189 184 181 173 169 147 133 128 123 117 109 106 10395 92 75 65 60 54 42 39 36 22 14 8 3 202 172 168 146 127 122 116 102 9164 59 53 2 203 126 121 101 204 98 99 100 205 206 207 208 209 210 211 212213 214 215 216 217 218 219 220 221 222 223]; (q) ϕ_(T)=[0 1 5 7 10 1213 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 5862 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108111 113 114 115 119 120 125 130 132 135 137 139 140 142 144 145 149 150152 153 155 157 158 159 160 161 162 164 166 167 171 175 177 179 180 183186 187 188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 3437 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118124 129 131 134 136 138 141 143 148 151 154 156 163 165 170 174 176 178182 185 190 192 195 198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106109 117 123 128 133 147 169 173 181 184 189 202 2 53 59 64 91 102 116122 127 146 168 172 203 101 121 126 204 100 205 98 99 206 207 208 209210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (r) ϕ_(T)=[199197 196 194 193 191 188 187 186 183 180 179 177 175 171 167 166 164 162161 160 159 158 157 155 153 152 150 149 145 144 142 140 139 137 135 132130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 7877 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 3129 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182178 176 174 170 165 163 156 154 151 148 143 141 138 136 134 131 129 124118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 3734 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169 147 133 128 123117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 202 172 168 146 127122 116 102 91 64 59 53 2 203 126 121 101 204 100 205 98 99 206 207 208209 210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (s)ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 4648 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 8889 90 94 97 105 108 111 113 114 115 119 120 125 130 132 135 137 139 140142 144 145 149 150 152 153 155 157 158 159 160 161 162 164 166 167 171175 177 179 180 183 186 187 188 191 193 194 196 197 199 200 4 6 9 11 1518 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96104 107 110 112 118 124 129 131 134 136 138 141 143 148 151 154 156 163165 170 174 176 178 182 185 190 192 195 198 201 3 8 14 22 36 39 42 54 6065 75 92 95 103 106 109 117 123 128 133 147 169 173 181 184 189 202 2 59100 101 116 121 126 127 146 172 205 64 99 122 168 206 91 209 53 102 203204 98 207 208 210 211 212 213 214 215 216 217 218 219 220 221 222 223];(t) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177 175 171167 166 164 162 161 160 159 158 157 155 153 152 150 149 145 144 142 140139 137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 8886 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 4644 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 200 198195 192 190 185 182 178 176 174 170 165 163 156 154 151 148 143 141 138136 134 131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 5549 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173169 147 133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3202 172 146 127 126 121 116 101 100 59 2 205 168 122 99 64 206 91 209102 53 203 204 98 207 208 210 211 212 213 214 215 216 217 218 219 220221 222 223]; (u) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 24 26 28 29 3133 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 72 73 74 77 7880 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119 120 125 130132 135 137 139 140 142 144 145 149 150 152 153 155 157 158 159 160 161162 164 166 167 171 175 177 179 180 183 186 187 188 191 193 194 196 197199 200 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 49 55 61 66 7176 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136 138 141 143148 151 154 156 163 165 170 174 176 178 182 185 190 192 195 198 201 3 814 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133 147 169 173181 184 189 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127 146168 172 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218219 220 221 222 223]; (v) ϕ_(T)=[199 197 196 194 193 191 188 187 186 183180 179 177 175 171 167 166 164 162 161 160 159 158 157 155 153 152 150149 145 144 142 140 139 137 135 132 130 125 120 119 115 114 113 111 108105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 67 63 62 58 5756 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 17 16 13 12 107 5 1 0 200 198 195 192 190 185 182 178 176 174 170 165 163 156 154 151148 143 141 138 136 134 131 129 124 118 112 110 107 104 96 93 87 84 8279 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201189 184 181 173 169 147 133 128 123 117 109 106 103 95 92 75 65 60 54 4239 36 22 14 8 3 202 2 53 59 64 91 98 99 100 101 102 116 121 122 126 127146 168 172 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217218 219 220 221 222 223]; (w) ϕ_(T)=[0 1 5 7 10 12 13 16 17 19 20 21 2426 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 63 67 68 69 70 7273 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113 114 115 119120 125 130 132 135 137 139 140 142 144 145 149 150 152 153 155 157 158159 160 161 162 164 166 167 171 175 177 179 180 183 186 187 188 191 193194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34 37 40 43 45 47 4955 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129 131 134 136138 141 143 148 151 154 156 163 165 170 174 176 178 182 185 190 192 195198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117 123 128 133147 169 173 181 184 189 202 2 59 100 101 116 121 126 127 146 172 205 5364 91 98 99 102 122 168 203 204 206 207 208 209 210 211 212 213 214 215216 217 218 219 220 221 222 223]; (x) ϕ_(T)=[199 197 196 194 193 191 188187 186 183 180 179 177 175 171 167 166 164 162 161 160 159 158 157 155153 152 150 149 145 144 142 140 139 137 135 132 130 125 120 119 115 114113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 72 70 69 68 6763 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 24 21 20 19 1716 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176 174 170 165 163156 154 151 148 143 141 138 136 134 131 129 124 118 112 110 107 104 9693 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 27 25 23 18 1511 9 6 4 201 189 184 181 173 169 147 133 128 123 117 109 106 103 95 9275 65 60 54 42 39 36 22 14 8 3 202 172 146 127 126 121 116 101 100 59 2205 53 64 91 98 99 102 122 168 203 204 206 207 208 209 210 211 212 213214 215 216 217 218 219 220 221 222 223]; (y) ϕ_(T)=[0 1 5 7 10 12 13 1617 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 57 58 62 6367 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105 108 111 113114 115 119 120 125 130 132 135 137 139 140 142 144 145 149 150 152 153155 157 158 159 160 161 162 164 166 167 171 175 177 179 180 183 186 187188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 30 32 34 37 4043 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112 118 124 129131 134 136 138 141 143 148 151 154 156 163 165 170 174 176 178 182 185190 192 195 198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103 106 109 117123 128 133 147 169 173 181 184 189 202 2 59 100 101 116 121 126 127 146172 205 64 99 122 168 206 53 91 98 102 203 204 207 208 209 210 211 212213 214 215 216 217 218 219 220 221 222 223]; (z) ϕ_(T)=[199 197 196 194193 191 188 187 186 183 180 179 177 175 171 167 166 164 162 161 160 159158 157 155 153 152 150 149 145 144 142 140 139 137 135 132 130 125 120119 115 114 113 111 108 105 97 94 90 89 88 86 85 83 81 80 78 77 74 73 7270 69 68 67 63 62 58 57 56 52 51 50 48 46 44 41 38 35 33 31 29 28 26 2421 20 19 17 16 13 12 10 7 5 1 0 200 198 195 192 190 185 182 178 176 174170 165 163 156 154 151 148 143 141 138 136 134 131 129 124 118 112 110107 104 96 93 87 84 82 79 76 71 66 61 55 49 47 45 43 40 37 34 32 30 2725 23 18 15 11 9 6 4 201 189 184 181 173 169 147 133 128 123 117 109 106103 95 92 75 65 60 54 42 39 36 22 14 8 3 202 172 146 127 126 121 116 101100 59 2 205 168 122 99 64 206 53 91 98 102 203 204 207 208 209 210 211212 213 214 215 216 217 218 219 220 221 222 223]; (aa) ϕ_(T)=[0 1 5 7 1012 13 16 17 19 20 21 24 26 28 29 31 33 35 38 41 44 46 48 50 51 52 56 5758 62 63 67 68 69 70 72 73 74 77 78 80 81 83 85 86 88 89 90 94 97 105108 111 113 114 115 119 120 125 130 132 135 137 139 140 142 144 145 149150 152 153 155 157 158 159 160 161 162 164 166 167 171 175 177 179 180183 186 187 188 191 193 194 196 197 199 200 4 6 9 11 15 18 23 25 27 3032 34 37 40 43 45 47 49 55 61 66 71 76 79 82 84 87 93 96 104 107 110 112118 124 129 131 134 136 138 141 143 148 151 154 156 163 165 170 174 176178 182 185 190 192 195 198 201 3 8 14 22 36 39 42 54 60 65 75 92 95 103106 109 117 123 128 133 147 169 173 181 184 189 202 2 59 100 101 116 121126 127 146 172 205 64 99 122 168 206 91 209 53 98 102 203 204 207 208210 211 212 213 214 215 216 217 218 219 220 221 222 223]; (bb)ϕ_(T)=[199 197 196 194 193 191 188 187 186 183 180 179 177 175 171 167166 164 162 161 160 159 158 157 155 153 152 150 149 145 144 142 140 139137 135 132 130 125 120 119 115 114 113 111 108 105 97 94 90 89 88 86 8583 81 80 78 77 74 73 72 70 69 68 67 63 62 58 57 56 52 51 50 48 46 44 4138 35 33 31 29 28 26 24 21 20 19 17 16 13 12 10 7 5 1 0 200 198 195 192190 185 182 178 176 174 170 165 163 156 154 151 148 143 141 138 136 134131 129 124 118 112 110 107 104 96 93 87 84 82 79 76 71 66 61 55 49 4745 43 40 37 34 32 30 27 25 23 18 15 11 9 6 4 201 189 184 181 173 169 147133 128 123 117 109 106 103 95 92 75 65 60 54 42 39 36 22 14 8 3 202 172146 127 126 121 116 101 100 59 2 205 168 122 99 64 206 91 209 53 98 102203 204 207 208 210 211 212 213 214 215 216 217 218 219 220 221 222223]; (cc) ϕ_(T)=[2, 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 3637 38 39 41 43 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81 83 85 8990 91 93 95 96 97 100 101 102 109 110 114 116 120 121 123 125 126 127128 129 130 131 135 136 142 145 147 152 157 158 165 168 171 173 175 178180 181 182 187 188 190 194 195 198 199 212 0 6 13 14 15 24 26 30 31 4048 53 54 60 63 68 72 73 80 84 86 87 88 92 98 104 106 111 115 134 137 139141 148 149 153 154 161 163 164 167 172 174 179 186 191 192 197 215 1 917 23 32 49 52 75 82 99 118 122 124 132 143 144 156 159 162 169 170 176183 185 189 196 204 34 42 44 45 46 65 105 108 112 155 166 207 4 61 119133 138 146 211 29 56 59 94 103 117 218 107 113 160 193 208 16 177 184200 69 150 210 50 203 151 202 140 201 209 214 66 205 206 213 216 217];(dd) ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173 171 168165 158 157 152 147 145 142 136 135 131 130 129 128 127 126 125 123 121120 116 114 110 109 102 101 100 97 96 95 93 91 90 89 85 83 81 79 78 7776 74 71 70 67 64 62 58 57 55 51 47 43 41 39 38 37 36 35 33 28 27 25 2221 20 19 18 12 11 10 8 7 5 3 2 212 197 192 191 186 179 174 172 167 164163 161 154 153 149 148 141 139 137 134 115 111 106 104 98 92 88 87 8684 80 73 72 68 63 60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189185 183 176 170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 4932 23 17 9 1 204 166 155 112 108 105 65 46 45 44 42 34 207 146 138 133119 61 4 211 117 103 94 59 56 29 218 193 160 113 107 208 184 177 16 200150 69 210 50 203 151 202 140 209 214 201 66 206 213 216 217 205]; (ee)ϕ_(T)=[2, 3 5 7 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36 37 38 39 4143 47 51 55 57 58 62 64 67 70 71 74 76 77 78 79 81 83 85 89 90 91 93 9596 97 100 101 102 109 110 114 116 120 121 123 125 126 127 128 129 130131 135 136 142 145 147 152 157 158 165 168 171 173 175 178 180 181 182187 188 190 194 195 198 199 212 0 6 13 14 15 24 26 30 31 40 48 53 54 6063 68 72 73 80 84 86 87 88 92 98 104 106 111 115 134 137 139 141 148 149153 154 161 163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 4952 75 82 99 118 122 124 132 143 144 156 159 162 169 170 176 183 185 189196 204 4 16 29 34 42 44 45 46 50 56 59 61 65 66 69 94 103 105 107 108112 113 117 119 133 138 140 146 150 151 155 160 166 177 184 193 200 201202 203 205 206 207 208 209 210 211 213 214 216 217 218]; (ff)ϕ_(T)=[199 198 195 194 190 188 187 182 181 180 178 175 173 171 168 165158 157 152 147 145 142 136 135 131 130 129 128 127 126 125 123 121 120116 114 110 109 102 101 100 97 96 95 93 91 90 89 85 83 81 79 78 77 76 7471 70 67 64 62 58 57 55 51 47 43 41 39 38 37 36 35 33 28 27 25 22 21 2019 18 12 11 10 8 7 5 3 2 212 197 192 191 186 179 174 172 167 164 163 161154 153 149 148 141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 7372 68 63 60 54 53 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176170 169 162 159 156 144 143 132 124 122 118 99 82 75 52 49 32 23 17 9 1204 4 16 29 34 42 44 45 46 50 56 59 61 65 66 69 94 103 105 107 108 112113 117 119 133 138 140 146 150 151 155 160 166 177 184 193 200 201 202203 205 206 207 208 209 210 211 213 214 216 217 218]; (gg) ϕ_(T)=[2, 3 57 8 10 11 12 18 19 20 21 22 25 27 28 33 35 36 37 38 39 41 43 47 51 55 5758 62 64 67 70 71 74 76 77 78 79 81 83 85 89 90 91 93 95 96 97 100 101102 109 110 114 116 120 121 123 125 126 127 128 129 130 131 135 136 142145 147 152 157 158 165 168 171 173 175 178 180 181 182 187 188 190 194195 198 199 212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 8084 86 87 88 92 98 104 106 111 115 134 137 139 141 148 149 153 154 161163 164 167 172 174 179 186 191 192 197 215 1 9 17 23 32 49 52 75 82 99118 122 124 132 143 144 156 159 162 169 170 176 183 185 189 196 204 3442 44 45 46 65 105 108 112 155 166 207 4 16 29 50 56 59 61 66 69 94 103107 113 117 119 133 138 140 146 150 151 160 177 184 193 200 201 202 203205 206 208 209 210 211 213 214 216 217 218]; (hh) ϕ_(T)=[199 198 195194 190 188 187 182 181 180 178 175 173 171 168 165 158 157 152 147 145142 136 135 131 130 129 128 127 126 125 123 121 120 116 114 110 109 102101 100 97 96 95 93 91 90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 5857 55 51 47 43 41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 75 3 2 212 197 192 191 186 179 174 172 167 164 163 161 154 153 149 148141 139 137 134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63 60 5453 48 40 31 30 26 24 15 14 13 6 0 215 196 189 185 183 176 170 169 162159 156 144 143 132 124 122 118 99 82 75 52 49 32 23 17 9 1 204 166 155112 108 105 65 46 45 44 42 34 207 4 16 29 50 56 59 61 66 69 94 103 107113 117 119 133 138 140 146 150 151 160 177 184 193 200 201 202 203 205206 208 209 210 211 213 214 216 217 218]; (ii) ϕ_(T)=[2 3 5 7 8 10 11 1218 19 20 21 22 25 27 28 33 35 36 37 38 39 41 43 47 51 55 57 58 62 64 6770 71 74 76 77 78 79 81 83 85 89 90 91 93 95 96 97 100 101 102 109 110114 116 120 121 123 125 126 127 128 129 130 131 135 136 142 145 147 152157 158 165 168 171 173 175 178 180 181 182 187 188 190 194 195 198 199212 0 6 13 14 15 24 26 30 31 40 48 53 54 60 63 68 72 73 80 84 86 87 8892 98 104 106 111 115 134 137 139 141 148 149 153 154 161 163 164 167172 174 179 186 191 192 197 215 1 9 17 23 32 49 52 75 82 99 118 122 124132 143 144 156 159 162 169 170 176 183 185 189 196 204 34 42 44 45 4665 105 108 112 155 166 207 4 61 119 133 138 146 211 16 29 50 56 59 66 6994 103 107 113 117 140 150 151 160 177 184 193 200 201 202 203 205 206208 209 210 213 214 216 217 218]; (jj) ϕ_(T)=[199 198 195 194 190 188187 182 181 180 178 175 173 171 168 165 158 157 152 147 145 142 136 135131 130 129 128 127 126 125 123 121 120 116 114 110 109 102 101 100 9796 95 93 91 90 89 85 83 81 79 78 77 76 74 71 70 67 64 62 58 57 55 51 4743 41 39 38 37 36 35 33 28 27 25 22 21 20 19 18 12 11 10 8 7 5 3 2 212197 192 191 186 179 174 172 167 164 163 161 154 153 149 148 141 139 137134 115 111 106 104 98 92 88 87 86 84 80 73 72 68 63 60 54 53 48 40 3130 26 24 15 14 13 6 0 215 196 189 185 183 176 170 169 162 159 156 144143 132 124 122 118 99 82 75 52 49 32 23 17 9 1 204 166 155 112 108 10565 46 45 44 42 34 207 146 138 133 119 61 4 211 16 29 50 56 59 66 69 94103 107 113 117 140 150 151 160 177 184 193 200 201 202 203 205 206 208209 210 213 214 216 217 218]; (kk) ϕ_(T)=[2, 3, 5, 7, 8, 10, 11, 12, 18,19, 20, 21, 22, 25, 27, 28, 33, 35, 36, 37, 38, 39, 41, 43, 47, 51, 55,57, 58, 62, 64, 67, 70, 71, 74, 76, 77, 78, 79, 81, 83, 85, 89, 90, 91,93, 95, 96, 97, 100, 101, 102, 109, 110, 114, 116, 120, 121, 123, 125,126, 127, 128, 129, 130, 131, 135, 136, 142, 145, 147, 152, 157, 158,165, 168, 171, 173, 175, 178, 180, 181, 182, 187, 188, 190, 194, 195,198, 199, 212, 0, 6, 13, 14, 15, 24, 26, 30, 31, 40, 48, 53, 54, 60, 63,68, 72, 73, 80, 84, 86, 87, 88, 92, 98, 104, 106, 111, 115, 134, 137,139, 141, 148, 149, 153, 154, 161, 163, 164, 167, 172, 174, 179, 186,191, 192, 197, 215, 1, 9, 17, 23, 32, 49, 52, 75, 82, 99, 118, 122, 124,132, 143, 144, 156, 159, 162, 169, 170, 176, 183, 185, 189, 196, 204,34, 42, 44, 45, 46, 65, 105, 108, 112, 155, 166, 207, 4, 61, 119, 133,138, 146, 211, 29, 56, 59, 94, 103, 117, 218, 107, 113, 160, 193, 208,16, 177, 184, 200, 140, 151, 201, 66, 205, 50, 209, 150, 206, 69, 202,203, 210, 213, 214, 216, 217].
 15. The method of claim 1, wherein thewireless transmitter comprises a wireless device or a network node. 16.A wireless transmitter comprising processing circuitry, the processingcircuitry operable to: encode a set of information carrying data bits uof length K with a linear outer code to generate a set of outer paritybits p along with the data bits u; interleave the set of outer paritybits p and the data bits u using a predetermined interleaving mappingfunction that depends on the number of data bits K and is operable todistribute some bits of the set of parity bits p in front of some databits u; and encode the interleaved bits using a polar encoder togenerate a set of encoded bits x.
 17. The wireless transmitter of claim16, the processing circuitry further operable to transmit the set ofencoded bits x to a wireless receiver.
 18. The wireless transmitter ofclaim 16, wherein the predetermined interleaving mapping functioncomprises a template interleaver for a largest value of K, referred toas K_(max), and the template interleaver comprises a high-index bitmapper wherein: the K data bits are loaded at the high-index positionsof the input of the template interleaver, where u=[u₀, u₁, . . . ,u_(K-1)] and the input of the template interleaver, denoted by v=[v₀,v₁, . . . , v_(K) _(max) ₋₁], is given by the following bit mapping:$v_{i} = \left\{ {\begin{matrix}u_{i - K_{\max} + K} & {{K_{\max} - K} \leq i < K_{\max}} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {otherwise}\end{matrix}.} \right.$
 19. The method of claim 16, wherein thepredetermined interleaving mapping function comprises a templateinterleaver for a largest value of K, referred to as K_(max), and thetemplate interleaver comprises a low-index bit mapper wherein: the Kdata bits are loaded at the low-index positions of the input of thetemplate interleaver in reverse, where u=[u₀, u₁, . . . , u_(K-1)] andthe input of the template interleaver, denoted by v=[v₀, v₁, . . . ,v_(K) _(max) ₋₁], is given by the following bit mapping:${v_{i} = \left\{ \begin{matrix}u_{K - 1 - i} & {0 \leq i < K} \\p_{i - K_{\max}} & {i \geq K_{\max}} \\{NULL} & {{othe}r{wise}}\end{matrix} \right.}.$ 20.-29. (canceled)
 30. The wireless transmitterof claim 16, wherein the wireless transmitter comprises a wirelessdevice or a network node.
 31. A method of operation of a wirelessreceiver in a wireless communication network, the method comprising:determining a decoder reaches a distributed CRC bit p_(i) when decodinga received set of polar encoded bits; calculating L estimated values,p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(

), determining whether the info bits associated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminating the decoding; upon determining there exists a successfulparity check, continuing the decoding.
 32. (canceled)
 33. The method ofclaim 31, wherein the wireless receiver comprises a wireless device or anetwork node.
 34. A wireless receiver comprising processing circuitry,the processing circuitry operable to: determine a decoder reaches adistributed CRC bit p_(i) when decoding a received set of polar encodedbits; calculate L estimated values, p_(i)(

), of the distributed CRC bit p_(i), one for each list

,

=0, 1, . . . , L−1; for each p_(i)(

), determine whether the info bits associated with p_(i)(

) leads to a successful parity check; and upon determining there is nosuccessful parity check for each p_(i)(

), terminate the decoding; upon determining there exists a successfulparity check, continue the decoding.
 35. (canceled)
 36. The method ofclaim 34, wherein the wireless receiver comprises a wireless device or anetwork node. 37.-38. (canceled)